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Official TSA Mathematical Questions (2008-2019)
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Official TSA Mathematical Questions (2008-2019)
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Speed as well as accuracy is important in this section. Work quickly, or you might not finish the paper. There are no penalties for incorrect responses, only marks for correct answers, so you should attempt all questions. Each question is worth one mark.
Calculators are NOT permitted.
Here you will find all TSA Mathematical questions that have been written 2008-2019.
A child’s bus fare is cheaper than the adult fare but is more than half the adult fare. The total cost of a single journey for an adult and two children is £1.20. Adult fares are all multiples of 10 p.
Explanation
The correct answer is C.
A child’s bus fare is cheaper than the adult fare but is more than half the adult fare: 0.5a<c<a. The total cost of a single journey for an adult and two children is £1.20: a+2c=1.20. We can substitute the values given from A-E into both equations until we get an answer that satisfies both equations. E.g for answer A we substitute ‘a’ with 0.30: 2c=1.20-0.30=0.90, so c=0.45, which does not satisfy 0.15<c<0.30, therefore A is not the correct answer. Only answer C satisfies both equations, 2c=1.20-0.50=0.70, so c=0.35, which satisfies 0.25<c<0.50, so is the answer.
Pierre and Marc are waiters. In one particular month, Pierre worked 30 sessions at the normal rate and 10 sessions at the overtime rate. Marc worked 20 sessions at the normal rate and 5 sessions at the overtime rate. At the end of this month, Pierre earned 700 Marc earned 425 euros.
Explanation
The correct answer is C.
If we let the pay for a session at the overtime rate=V and the pay for a session at the normal rate=N, we can form a pair of simultaneous equations, one for each of Pierre’s and Mark’s total pay: 30N+10V=700 and 20N+5V=425. We can solve these by doubling the second equation (representing Mark’s pay), so it becomes 40N+10V=850, and then subtract the equation representing Pierre’s pay from this: (40N+10V=850)-(30N+10V=700)–>10N=150–>N=15=the normal rate per session. Substitute this value into any of the equations to find a value for V, the overtime rate per session, for example: (30×15)+10V=700–>450+10V=700–>10V=250–>V=25.
The chart below shows the distribution of results this season for the Arlsea Strikers hockey They have played 24 matches to date and lost none.
Explanation
The correct answer is E.
Matches they have won=home wins+away wins, which together have an angle of 270 degrees in the pie chart, which is 3/4 of the total pie chart. So the total number of wins is given by: 24×3/4=18.
Inflation in Bolandia has been a steady 10% per year for many years. Evitan, a Bolandian citizen, bought his car one year ago for 500 Bols. He now wants to trade in his car for an identical model. He can expect to receive 80% of the current new value of his existing The price of new models has increased in line with inflation.
Explanation
The correct answer is E.
As inflation is 10% per year, and he is purchasing the same model as he did one year ago, the price of the car would have risen by 10%, from 500 to 550bols (500×1.10=550). He would receive 80% of the new value of his car, which is now 550bols, so it would be 550×0.80 (or 550×4/5)=440bols. Therefore, he extra money he is spending would be 550-440=110bols.
I am resurfacing my driveway using bricks in the pattern shown below. The visible part of the brick measures 10cm by 20cm. To achieve a rectangular shape, part of some of the bricks must be cut off. The part which is cut off can be used elsewhere on the drive. The diagram shows that eight bricks would be required to cover an area 40cm by 40cm:
Explanation
The correct answer is B.
As 550 is a multiple of 10 and 400 is a multiple of 20, we will have an exact number of bricks that will fit. As the parts of the bricks which are cut off can be used elsewhere on the drive, we only need to consider the total number of bricks. The total area of the rectangular drive would be: 550×400=220000cm^2. The area of a single brick is: 20×10=200cm^2. Therefore, the number of whole bricks required is: 220000/200=1100.
John has 15kg of general potting compost which is made up of 1/3 sand and 2/3 coir. He wants compost to repot some conifers which require a better draining mixture of 60% sand to 40% coir.
Explanation
The correct answer is B.
His 15kg of general potting compost consists of 15/3=5kg of sand and 15-5=10kg of coir. We can use trial by error of the answer options given until we get the correct ratio of sand to coir as 3:2. If we add 5kg of sand, the ratio becomes 10:10=1:1, which is not want we want. Adding 10kg, the ratio becomes 15:10=3:2, which is what we want, therefore B is the answer.
Peter needs to separate his sheep into 16 squares. Each side of a pen is formed by a free-standing barrier known as a hurdle. Each pen must be individually accessible on at least one side so that sheep can be penned or released without a risk of the others escaping.
Explanation
The correct answer is B.
To use to minimum number of hurdles, we must make the pens ‘share’ the maximum possible number of hurdles, whilst keeping each pen individually accessible on at least one side. To do this we must form two back-to-back lines of square pens, i.e. a 8 by 2 grid. This would require 42 hurdles in total, which is B.
A piece of ribbon 8m long is folded in half so the two ends are on top of each other. This doubled 4m length is then folded in half again. The folded, 2m length of ribbon is then cut right through at its midway point.
Explanation
The correct answer is C.
Draw out the ribbon at each successive stage. This should show you that cutting through the folded 2m ribbon would make 4 cuts in the ribbon. This would give 5 pieces of ribbon, and as only answer C gives this number it must be the correct answer.
Mohammad Eisa Ali
Medicmind Tutor
Tue, 25 Jan 2022 15:48:45
Shouldn't be 4? Anyone explain the reasoning.
dddd
Medicmind Tutor
Fri, 12 Aug 2022 13:47:57
ummmm . what
anon
Medicmind Tutor
Sun, 15 Oct 2023 15:12:22
how is it not E?
A small mail order company sends out three sizes of parcel in about equal numbers which require postages of 24c, 30c and 72c. They stock stamps in denominations of 6c and 30c and use the minimum number of stamps on each parcel.
Explanation
The correct answer is C.
The first step is to work out how the required postages of 24c, 30c and 72c are made up using the minimum number of stamps. For 24c we can see that this must be made up of 4 units of the 6c stamps, while the 30c postage is met by a single 30c stamp and the 72 postage by 2 units of the 30c and 2 units of the 6c stamps. Overall, since the three sizes of parcel are sent out in equal numbers, this ratio comes to 6 units of the 6c for every 3 units of the 30c stamps. This simplifies to 2 units of the 6c for every 30c stamp. Therefore, answer option C is correct.
Jess buys two lengths of carpet in the sales. The carpet is 4m wide and one of the lengths purchased is 4m long while the other is 6m. There is a very pronounced pattern which means that the pieces can only be joined so that the pattern runs the same Jess will only accept one join.
Explanation
The correct answer is E.
Since one of the lengths of carpet bought by Jess measures 4m by 4m, any room where both the sides are greater than 4m will require more than one join. Since Jess will accept only one join, this means that one of the sides of the room has to be 4m or less and therefore the only room that can be carpeted is the library as one of the sides of the floor measures 4m.
In a prize weight-lifting competition the winner receives $100 if he lifts 80kg. He then receives $10 for the next 5 additional kg, $15 for the second, and the incremental prize money increases by a further $5 for each additional unit of 5kg he successfully lifts.
The winner of the competition lifts 110kg.
Explanation
The correct answer is C.
The winner lifts 30kg more than 80kg, which means that they will receive incremental prize money for the 6 additional units of 5kg that they have lifted. This adds up to 100+10+15+20+25+30+35= $235 and hence the answer is C.
A manufacturer wishes to make an open-topped box out of the piece of cardboard shown below by folding up its sides.
Explanation
The correct answer is C.
Folding up the sides takes 2 lots of 5cm off each side and gives the box a height of 5cm, making the dimensions in cm: 50-(5×2) by 50-(5×2) by 5 = 40 by 40 by 5. So the colume would be 40x40x5=8000cm cubed.
The petrol tank of Jenny’s car holds 50 litres of petrol. A warning light comes on when only 5 litres are left. She always fills it as soon as she can after the warning light comes The car travels 100km on 8 litres of petrol. Last time she put petrol in, which she was able to do immediately after the light came on, she only had $6 with her so she spent it all on fuel at 60c per litre. She then drove 50km and saw a new garage offering petrol at 50c per litre – an offer too good to miss. She filled the tank completely and paid with her credit card.
Explanation
The correct answer is C.
She last put fuel in just as the light came on, so when there was 5L left in the tank. She spent $6 on 60c per litre, which would have given her: 6/0.60=10L more of petrol, so at this point there would be 15L in her tank. Next she drove 50km which would have used 4L of petrol (as the car travels 100km on 8L), so her tank would then contain 15-4=11L. She then filled the tank, which means 50-11=39L, at 50c per litre, which would have cost: 0.50×39=$19.50.
A boy is given $1.00 by his grandparents to buy sweets. He decides to spend at least half his money on gobstoppers at 5c each, at least a quarter of his money on fruit chews at 3c each and at least one tenth of his money on pieces of bubble gum at 2c each. He will decide how to spend the rest of the money when he gets to the shop.
Explanation
The correct answer is B.
To find the lowest and highest possible numbers of bubble gum pieces he can buy, we need to calculate the lowest and highest possible amounts of money (respectively) that he could have spend on them. He has to spend at least one tenth of his money on bubble gum, which would be:1/10=$0.10=10c, so this is the lowest possible amount he can spend on bubblegum. Therefore the lowest number of bubble gum pieces he can buy at a cost of 2c each is: 10/2=5 pieces. Eliminate answers C, D and E because their lower bound is not 5. To calculate the maximum number of bubble gum pieces he can buy, we need to spend the lowest possible amounts on gobstoppers and fruit chews, leaving us with the maximum amount of money possible to spend on bubble gum. The minimum amount he can spend on gobstoppers is half of his money (50c, which would buy 10 gobstoppers) and that for fruit chews is a quarter of his money (25c). But since each fruit chew costs 3c, he would have to spend at least 27c on fruit chews in order to spend at least a quarter of his money on them. This would leave him with: 100-(50+27)=100-77=23c left to spend on bubble gum. As each piece costs 2c, he could buy: 23/2=11.5 pieces, but since he cannot buy half of a piece, he can buy a maximum of 11 pieces of bubble gum.
The diagram shows three pulleys driven by belts. Pulley A and the small, inner pulley at B are 1 m across, the outer pulley at B is 2 m across and pulley C is 4 m across.
Explanation
The correct answer is A.
Mohammad Eisa Ali
Medicmind Tutor
Wed, 26 Jan 2022 15:34:59
Explanation is missing here.
A small restaurant is open for 45 weeks each It employs 6 people at total wages of £1200 per week (they are not paid when the restaurant is closed). It is open for lunch on Monday to Friday and dinner on Tuesday to Saturday and on average 20 people eat at each opening. The owners pay rental on the premises of £36 000 per year. Other expenses (insurance, gas electricity, water, rates etc.) come to £9000 per year. The cost of buying food works out at £5 per meal served.
Explanation
The correct answer is C.
The restaurant employs 6 people at total wages of £1200 per week for 45 weeks which would cost:1200×45=£54000. It is open for lunch on Monday to Friday (5 times a week fro lunch) and dinner on Tuesday to Saturday (5 times a week for dinner), so it is open 10 times a week in total. As on average 20 people eat at each opening and each meal would cost £5 to make, this would cost: 20(people)x10(opening per week)x45(weeks open)x5(cost per meal)=£45000. Additional costs are rental at £36000 per year and other expenses at £9000 per yr. Therefore the total cost for a year would be: 54000+45000+36000+9000=£144000. The number of meals sold per year would be: 20x10x45=9000, so the cost of each meal would need to be: 144000/9000=£16 to cover expenses.
A rainwater butt in Joan’s garden fills from a flat roof of an equivalent area to 25 square The butt holds 200 litres and is full when Joan starts using it in the summer. During the gardening season, 160 litres falls on each square metre of roof. Only half of this is collected as the rest evaporates. Joan uses 100 litres from the butt to top up her garden pond each week for 25 weeks. If there is not enough water in the butt, she completes the job with mains water which is rather expensive. During the summer months there is never enough rain to overfill the butt.
Explanation
The correct answer is B.
We are told that during the gardening season 160 litres of rain fall on each square metre of the roof. Since half will evaporate, we can divide this by 2 to give 80 litres per square metre and multiply by 25 to get the total volume collected over the whole roof, giving us 2000 litres. Since the butt never overfills, we can be confident that Joan will be able to use the total 2000 litres. In addition, the butt was already full at the beginning of the season, giving us an additional 200 litres. So overall she is able to use 2200 litres from the rainwater butt. By contrast, she needs 100 litres every week for 25 weeks to top up the garden pond, so she requires 2500 litres over the season. This means that she needs to use 300 litres of mains water to complete her work, and therefore the correct answer option is B.
Splashford Swimming Pool charges £2 per session for adults and £1 for children.
Also available is a Family Swimcard. At a cost of £50, the Family Swimcard allows unlimited use of the pool for one year for 2 adults and up to 3 children. For larger families, every additional child must pay half the children’s rate each time.
Mr and Mrs Teal and their 4 children are keen swimmers. They used their Swimcard when the family went swimming 40 times last year.
Explanation
The correct answer is D.
To calculate the charge if they payed per session, first calculate the cost of the family to swim for a single session: (2 adults x £2) + (4 children x £1)= 4+4=£8 per session for the whole family. They swam 40 times so this would have cost: 40 x 8 =£320. When using the swimcard, the family must also pay half the price for a single child each time (as they have 4 kids and the swimcard only pays for 3). Therefore the total cost for the year would be: 50+(1/2 x 40)= 50+20=£70. So the total amount saved using the swimcard instead of paying per session is: 320-70=£250.
Sue and Ben are buying some kitchen goods at a shop which is having a sale. The terms of the sale are as follows:
The marked prices of the goods they have chosen come to £96.
Explanation
The correct answer is D.
Spending £96 would give a 33% reduction which means they would have to pay for 67% or approximately 2/3 of £96: 96 x 2/3 =£64. Spending an additional £6 means they would spend 96+6=£102, which would have a 50% reduction, which would be: 102 x 1/2 =£51 payed. The difference between these is: 64-51= £13..
I have been asked to move 120 boxes weighing 25kg each and 90 boxes weighing 20kg each from the ground floor to the fifth floor of the office block in which I work. Unfortunately, nobody is available to give me any help.
There is a sign in the lift which reads:
I weigh 80kg.
Explanation
The correct answer is D.
For this question we can see that once we take away the weight for the person from the maximum load, we can transport 320kg worth of boxes in each trip. In order to take the minimum number of journeys, we will have to ensure that we take the maximum load in each trip. Since 25kg boxes alone cannot make 320kg on their own, we can start off with transporting 300kg worth of the 25kg boxes with an additional 20kg box for each trip until we finish the 25kg boxes. Since 300/25 = 12, this means that we’ll be transporting 12 units of the 25kg boxes and 1 of the 20kg boxes for each trip initially. Since 120/12=10, this means that it will take us 10 trips to finish off the 25kg boxes (during which time we will have transported 10 of the 20kg boxes). For the remaining trips we will only transport the remaining 80 units of the 20kg boxes. Since 320/20= 16 we can transport 16 of the 20kg boxes per trip and 80/16 = 5 so this will take 5 trips. Overall, we therefore need a minimum of 10+5 = 15 trips and the answer is D
A taxi service advertises its rates for travel to the local airport as shown below:
Explanation
The correct answer is D.
For this question it is easiest if we calculate the actual cost per person for different numbers of passengers. For 1 passenger we can see that it is £70. For 2 passengers it will cost £70+£10=£80 which can be split between the 2 passengers, giving £40 per person. Carefully observing the graphs using the ruler shows that the only graph where the cost for two passengers actually lines up perfectly with £40 (rather than being slightly above or slightly below) is graph D, which is the correct answer.
A secretary is in a bad mood with her boss and has to write three letters intended for three different people. She makes sure that each of the recipients of the letters will receive one written to someone else.
Explanation
The correct answer is B.
If we consider the three recipients to be persons A, B and C, and the corresponding letters that they were meant to receive as letters a, b and c, we can easily and quickly work out the possible combinations. Since each of the recipients can only receive a letter intended for the other two, this means that A can only receive letters b or c. If we start of with A receiving b, we can see that the only combination where this will work is if B then receives c and C receives a, as C cannot receive letter c. The only other letter A can receive is letter c, and again we can see that the only combination in which this would work is if B receives a and C receives b because B cannot receive letter b. Therefore, there are only 2 possible combinations and the answer is B.
The graph below shows Mr Evans’ bank balance at the end of each month in a year.
Explanation
The correct answer is D.
An important factor to remember about this question is that while the initial graph shows the balance at the end of the month, the answer options show the change during the month. This means that the initial bar in the answer option graphs is not meaningful to us since we have no information on the previous December’s bank balance so we cannot determine whether the bank balance increased or decreased during January. So we can simply ignore the first bar. However, we can see that the bank balance at the end of February is lower that that at the end of January, so clearly the bank balance must have decreased during February. This alone allows us to exclude answer options B and E. We can then scan the remaining answer options (A, C and D) to check where the graphs next differ, which is during July. We can see that the bank balance at the end of July is the same as at the end of June, hence there must have been no change during July, so we can exclude A. C and D next differ during December. Since the bank balance at the end of December is greater than that at the end of November, the balance must have increased during December hence the correct answer is graph D.
Fred, Joe and Bill do plumbing, electrics and plastering respectively and work together on certain building jobs. They will each take on any job involving all three types of work, sub-contract to the others where necessary and sort out any payments at the end of the month.
At the end of March, Bill has done £300 of work for Fred and £200 of work for Joe. Joe has done £100 of work for Fred and £250 of work for Bill. Fred has done £150 of work for Joe and £200 of work for Bill.
Explanation
The correct answer is B.
Working in order of how it is given in the passage and using F, J and B to represent Fred, Joe and Bill respectively, we can write ‘-‘ for when someone owes a another person money and ‘+’ when someone is owed money. E.g. B is owed 300 from F and 200 from J, so this can be written as B=+200+300, J=-200, F=-300. Doing this for all of the statements given leaves: B=+200+300-250-200=+50, J=-200+100+250-150=0, F=-300-100+150+200=-50. Therefore overall Bill is owed £50 and Fred owes £50, and this can be settled by Fred giving Bill £50.
The fuel consumption of Ted’s new car is given in the manufacturer’s data sheet as follows:
The cost of fuel is 80c per litre. Ted’s journey to work consists of 20km on country roads normally at 90km/h, 40km on motorway at 110km/h and 20km in town at 50km/h.
Explanation
The correct answer is B.
First, calculate the total consumption. 20km at 90km/h: 6/5litres (divide by 5 because the consumption is given per 100km, and 20km is 1 fifth of 100km). 40km at 110km/h: 6.5×4/10=13/5litres. 20km at 50km/h: 7.5/5litresm (leave as fraction over 5 to make next calculation easier). Total consumption: 6/5+13/5+7.5/5=26.5/5 OR 5.3litres. Cost:5.3X0.80=$4.24
Maggie is preparing 300 information packs so that she can respond to enquiries for her holiday cottages. Each pack contains:
• A basic information sheet – this is printed on A4 sized paper on both sides so that it may be folded to form 4 pages.
• A sheet with prices on one side and a booking form on the other – two of these are printed on a sheet of A4 paper which is then cut in two.
• An A4 information sheet giving details of some local amenities – this is printed on one side only.
• A single A4 sheet colour brochure printed on both sides – this is provided free by the local Angling Association.
The local printer charges 2p per side of A4 for reproduction.
Explanation
The correct answer is B.
First, calculate how many sides of A4 are needed for a single pack. The number of sides of A4 would be: 2 for the basic info sheet, 1 for booking and prices (as each use half of a side of A4), 1 for details of some local amenities and 2 for the brochure (but this is free so must be ignored in the following calculations). Altogether this would be: 2+1+1+=4 sides of A4 that need to be paid for to make a single pack. 300 packs are needed so this would be: 300×4=1200 sides of A4 that need to be paid for in total. At 2p per side, this would cost: 1200×0.02=£24.
The coffee machine in our office offers a choice of regular or decaffeinated coffee; black or with one of three sorts of milk (full, semi-skimmed, skimmed); and, for those who want sweetening, either one or two spoonfuls of sugar or one or two non-sugar sweetening tablets.
Explanation
The correct answer is D.
The choices can be split into 3 categories: caffination, colour (milk) and sweetening. There are 2 options for caffination (regular or decaf), 4 options for colour (no milk, skimmed, semi-skimmed or full) and 5 options fro sweetening (no sweetening, 1 sugar, 2 sugars, 1 sweetner, 2 sweetners). Therefore the calculation would be 2x4x5=40.
To play a football pools game, participants must select four matches from the fifty on the coupon. Points are scored depending on the result of each match as follows:
If the home team wins, the participant scores 1.0 point
If the away team wins, the participant scores 1.5 points
If the match is a draw, the participant scores 3.0 points
Explanation
The correct answer is C.
The totals other than C can be made as follows: A=1+1.5+3+3=8.5, B=1.5+1.5+3+3=9, C=1+3+3+3=10, D=1.5+3+3+3=10.5.
Jars of Bestcaff coffee weighing 200g are normally £2.50 at Kostless and Savemore, but both supermarkets have a special offer this week:
Explanation
The correct answer is A.
Cost for 200g at Kostless: 2.50-0.80=1.70; therefore for 1000g (which=200gx5) it would cost 1.70×5=£8.50. If we want 1kg from Savemore, we need to find the weight so that 25% extra would give us 1kg in total. Let this weight be ‘y’: y x 1.25 = 1000g. Therefore y=1000/1.25=1000×4/5=800g. At £2.50 per 200g, this would cost: 2.50×4=£10. Therefore, the cost difference per kg would be: 10-8.50=£1.50.
When my father ran a pizza shop he sold pizzas for a fixed amount plus an amount proportional to the ingredients used. A regular pizza uses twice the ingredients of a mini one and a large pizza twice those of a regular one.
Explanation
The correct answer is E.
Form 3 simultaneous equations, one for the cost of each size pizza. Let y be the fixed amount and let x be the amount proportional to the ingredients used on the mini pizza. Mini: y+x, Regular: y+2x (as it has 2 times the amount of ingredients as the mini) and Large: y+4x (as it has 2 times the amount of ingredients as the regular). To find the answer, equate each simultaneous equation to its corresponding price, (e.g. for answer A: y+x=0.49, y+2x=1) and see if the solutions work for all three equations, in which case you will have found the answer. The only trio of prices that give such solutions are in answer E: y+x=2, y+2x=3, subtracting the 2nd equation from the 1st gives x=1 and substituting x=1 into the first equation gives y=1. Then see if these solutions work for the 3rd equation by substituting them into: y+4x, which gives a value of 5, which is the 3rd price given in E. Hence E is the answer.
I often order items from a mail order catalogue. The charges for postage and packing (to be added to the order value) are as follows:
Order value: less than £25.00 – £4.50
£25.00 to £49.99 – £8.50
£50.00 to £74.99 – £12.00
£75.00 to £99.99 – £15.00
£100.00 and over – £17.50
Just before sending off my latest order, I noticed that the current catalogue offers half price postage and packing for orders of 8 or more items. My order was for 7 items, with an order value of £74.60. I could not find anything else I wanted, so I just added the cheapest item in the catalogue (priced at £1.25) to my order.
Explanation
The correct answer is A.
Without adding the extra item to the order, the total cost would have been: 74.60+12.00=86.60 . When adding the extra item, the order value would increase to 74.60+1.25=75.85, and the postage and packaging value would increase to 15.00, however because she now has 8 items this value would be halved, meaning the postage and packaging would cost 7.50.I In total this gives: 75.85+7.50=83.35. The difference between the total cost with the extra item compared to without therefore would be: 86.60-83.35=3.25 .
I am a member of a book club. Every month I must choose at least one book. All books are sold at a discount of £2.00 on shop prices. I pay a fixed charge for postage regardless of which books I order.
Explanation
The correct answer is C.
anon
Medicmind Tutor
Tue, 26 Sep 2023 11:50:58
why does buying one book not give you savings of £2?
James
Medicmind Tutor
Tue, 10 Oct 2023 17:08:11
I think because the postal charge must be $2 - this is the trick. That is why it says 'could show' - all the others seem more likely but have little errors meaning they are unlikely, whereas C seems unlikely but in this unlikely scenario it actually works
Over the course of a year, Mr and Mrs Jones and their two sons spend an average of £120 a week at the local supermarket. 70% of this spending is the weekly family food bill, 20% goes on household goods and the final 10% on store-cupboard ingredients. When their daughter returns from her gap year to live at home, the weekly food bill increases by 20% and their spending on household goods goes up 5%, whilst they continue to spend the same on store-cupboard ingredients.
Explanation
The correct answer is B.
Spendings without the daughter: food bill=0.7×120=84, household goods=0.2×120=24, store-cupboard=0.1×120=12. Spendings with daughter: food bill=84×1.2=100.80, household goods=24×1.05=25.20, store-cupboard=12. Total spendings when daughter is home: 100.80+25.20+12=138. To make these calculations simpler, you may wish to multiple by fractions instead (eg. 84×6/5=100.80) or find the percentage added and add this to the original (20% of 84 is 10%x2=8.4×2=16.80, then 16.80+84=100.80).
A merchant bank recently advertised for new graduates to fill positions as trainee analysts; 230 people applied. Of these, 127 had maths as a component of their degree and 89 had economics as a component of their degree. Only 45 had neither maths nor economics as a component of their degree.
Explanation
The correct answer is B.
Draw a venn diagram consisting of two overlapping circles, one labelled M (maths) and the other labelled E (economics). 45 people did neither M or E so write 45 outside the circles. There were 230 people altogether, so the total number of people inside the circles (which either have M or E or both) would be: 230-45=185. To calculate the number of people in the overlapping segment (who have both M and E), we need to find the difference between the total number of people inside the circles (185) and the number of people who have M + E: (127+89)-185=216-185=31 people.
Alan bought a silver jug at an auction for £80. A year later, the price of antique silver had risen and he decided to sell it at auction, for which he received £100. He immediately regretted his decision and approached the buyer, who sold it back to him but he had to pay £110. Another year later, he needed some money so sold the jug to a dealer for £120.
Explanation
The correct answer is C.
We can find the answer by thinking of each number given as either a loss(-) or a gain(+) in reference to Alan. He bought the jug for £80, which is a loss. He sold it for £100 (gain). He bought it again for £110 (loss). He sold the jug again for £120 (gain). Altogether: -80+100-110+120=£30.
Today I am going to treat my lawn with Greatgrass liquid lawn The instructions on the bottle tell me to dilute 1 part Greatgrass with 15 parts water, then apply evenly. Three hours later the treatment should be repeated, but with a mixture of 1 part Greatgrass and 24 parts water. I have worked out that I need to make up a total of 12 litres of diluted liquid for each application.
Explanation
The correct answer is B.
For the first application, 1/16th of the 12 litre dilution will be Greatgrass, which would be a volume of 12/16=3/4=0.75 litres=750ml. For the second application, 1/25th of the dilution will be Greatgrass, which is 12/25, which can be more easily calculated by converting the 12 litres into ml: 12000/25=2400/5=480ml. Total Greatgrass used: 750+480=1230ml.
The mock examination and actual GCSE results for English in one year at Morgan College are shown below:
|
|
Actual GCSE exams | ||
| Grades A-C |
Other Grades |
||
|
Mock GCSE exams |
Grades A-C | 90 | 25 |
| Other grades | 25 |
60 |
|
Explanation
The correct answer is E.
Total number of pupils=90+25+25+60=200. Those who had their GCSE results correctly predicted by their mocks would either have ‘grades A-C’ (value in the top left corner of the table) for both or ‘other grades’ for both (value in the bottom right corner of the table). Adding these values and dividing by the total number of pupils: (90+60)/200=150/200=75%.
When Anton joined the company that he works for, 8 years ago, his salary was £29000. Each of his 8 annual salary increases has been 10% of his previous salary rounded up to the next multiple of £500.
Explanation
The correct answer is C.
We need to multiply Anton’s new salary by 1.1 (or add on 10% of the value) each year for 8 years following his initial salary (in year 1), after rounding up to the next multiple of 500. To calculate the salary in the second year: 29000×1.1=31900, which is 32000 rounded up to the next 500. For the third year: 32000×1.1=35200, which is 35500 to the next 500. We do the same for the following years up to the 8th year: 4th=35500×1.1=39050~39500, 5th=43450~43500, 6th=47850~48000, 7th=52800~53000, 8th=58300~58500, 9th (we need to do 9th because there are 8 increases, so 9 different salaries in total) =64350~64500.
The diagram shows the dimensions of an office and entrance I wish to carpet them. Each must have a single piece of carpet with no joins, but I can use two separate pieces for the two rooms. As I intend to do it as inexpensively as possible, I will buy an offcut.
Explanation
The correct answer is C.
If we rotate the room on the left in the diagram so that the 2.2m sides are oriented vertically and the 1.8m sides are horizontally, we can limit the width of the carpet we need to purchase, as the 2.2m sides would be included as part of the 4.2m side, whereas the 1.8m side would need to be added to the 2.6m side of the room on the right. This would give us dimensions of 4.2m by (2.6+1.8=)4.4m, which is answer C.
Standard 100W light bulbs cost 40p each and are expected to last for 2 years in average use. Low power equivalent brightness bulbs cost £10 each, are expected to last for 8 years and use only A 100W lightbulb operated for 10 hours will use 7.5p of electricity. A 20W bulb will operate for 50 hours on the same amount of electricity. I have a light in my living room which is on for about 20 hours per week. Next time the living room bulb breaks, I will buy a low wattage bulb instead of a standard one.
Explanation
The correct answer is C.
As £10 – 40p = £9.60, this means that it costs £9.60 more to buy the low power lightbulb and we therefore need to calculate how long it will take before we are able to recover this extra £9.60.
We are told that a 100W lightbulb uses 7.5p of electricity in 10 hours. This means that within 20 hours (the amount of time that the lightbulb is used for per week) this will cost 15p of electricity. By contrast the 20W lightbulb is said to use the 7.5p of electricity for 50 hours which means that it uses 7.5/5 =1.5p per 10 hours so 3p for every 20 hours. Hence per week, the 100W lightbulb would have used 15p while the 20 W uses 3p and we therefore save 12p each week. To work out how many weeks it will take before we save enough to recover the extra purchase cost, we can do 960p/12p=80 weeks and the correct answer is C.
Three thermometers are each accurate to within 2 degrees above or below the temperature they actually One reads 7°, one reads 9° and one reads 10°.
Explanation
The correct answer is D.
First, find the lower and upper bounds for the range of each thermometer by subtracting and adding 2 degrees to the temperature shown on each thermometer respectively. The ranges are: for the 7 degree thermometer=5-9, for the 9 degree one=7-11 and for the 10 degree one=8-12. The maximum range is found by finding the highest and lowest temperature possible out of all the thermometers, which is 5-12 degrees. To find the minimum range, you find the lowest upper bound of range (which is 9 degrees, the upper bound of the 7 degree thermometer) and the highest lower bound of range (which is 8 degrees, the lower bound of the 10 degree thermometer). Therefore the minimum possible range is 8-9 degrees.
I have just joined a savings I will pay in £50 each month and at the end of each complete year I will be paid 5% interest on my average balance (i.e. the average of my starting and finishing amount) for the previous 12 months.
Explanation
The correct answer is B.
The balance at the end of the first year after the £50 deposits will be £50×12 = £600. This means that the average balance for that year after averaging the starting (£0) and finishing amount (£600) will be £300. 5% of this will be £15, so the complete balance at the end of the first year after the interest has been paid will be £615. The next year he will continue to pay in £50 per month, so the balance at the end will be £1215. To calculate the interest at the end of the second year: the average balance will be (£615+£1215)/2=£915. 5% of £915 is about £45 (£45.75 to be exact but it is unnecessary to calculate this as the answers are rounded to the nearest £10) £1215+the interest of £45 = £1260 giving us the correct answer of B.
Every Thursday, Marilyn spends 10 hours making 60 cakes to sell at her local market. The cost of the ingredients to make each cake is £1.60 and Marilyn charges £6 an hour for her time. She usually sets the sale price for a cake at 75% more than the total costs of making However, when she sells to her friends she gives them a 10% discount on the normal sale price.
Explanation
The correct answer is B.
Time taken to make one cake= 10hrs/60cakes= 1/6hrs. Charge for time per cake= 1/6hrsx£6=£1. Total cost of making one cake=charge for time+cost of ingredients=£1+£1.60=£2.60. Regular sale price for 1 cake=£2.60×1.75 (or £2.60+ 75%), which can be calculated by finding a quarter (25%) of 2.60 by dividing by 4, which gives 0.65, and then multiplying this by 3 to get 75%, which gives 1.95, and then adding this to the original 2.60, which gives £4.55. Then to calculate the discount price, the calculation would be £4.55×0.90, which can be calculated by finding 10% of 4.55, which is 0.455, and then subtracting this from the original price to find 90%: 4.55-0.455=4.095, which is £4.10 to the nearest penny.
Mr Daley has bought some used carpeting for his new 24 m x 12 m car showroom. The carpet is in 8 m x 4 m rectangles which will be joined using a strip of double-sided tape along all seams. Additionally, double-sided tape will be needed to stick the carpet around the edges of the showroom.
Explanation
The correct answer is C.
9 lots of the 8mx4m carpet will cover the floor of the room in a 3 by 3 arrangement. Therefore, Mr Daley will need tape to stick the carpet down around the edges of the room which is= 24+12+24+12=72m of tape, as well as tape for the seams between the different carpet segments, which will be an additional 24+24+12+12=72m of tape. Therefore, the minimum amount of tape he will require is 72+72=144m of tape, giving us the correct answer option of C.
An acre of land planted with sugar beet produces 550 gallons of ethanol from the sugar by A car converted to run on E75 (a 75% ethanol, 25% petrol mixture) can do 40 miles per gallon.
Explanation
The correct answer is B.
If you drive 20,000 miles at 40 miles per gallon, you need: 20,000/40=500 gallons. 75% of this is ethanol: 500×0.75=375 gallons of ethanol. 550 gallons of ethanol are produced per acre of land, so the number of acres of land needed can be calculated by: 375/550=0.68= answer B.
The graph below shows the additional financial value of repeated applications of fertiliser applied to crops in a field for a year. For example, two applications gives £2,000 more value to the crop than one application.
Explanation
The correct answer is C.
For ease of calculation, assume the initial value of the crop with no applications is zero. After 1 application, the cost is 1000 and the additional value of the crop is 500, so the profit would be 500-1000=-500. For 2 applications, the cost is 2000 and the total additional value would be the sum of the additional values after 1 and 2 applications (500+2000)=2500, so the profit would be 2500-2000=500. Use similar calculations to work out the profit for 3 applications: (500+2000+1500)-3000=4000-3000=1000. For 4 applications: (500+2000+1500+500)-4000=4500-4000=500. Therefore the maximum profit would be after 3 applications, because the additional value of crop per application for 4+ applications is below 1000, so the profit would begin to decline per additional application.
When travelling in Kromistan and not understanding the currency, I offered a red note for an item marked ‘135K’. I was given, in change, three green coins and one blue Later, for a newspaper marked ’33K’, I offered a handful of coins and the vendor took four green and one blue. There are only these three denominations of money available; the smallest is marked ‘1K’ and each higher denomination is a whole number multiple of the lower denominations.
Explanation
The correct answer is B.
Form the following simultaneous equations from the information given using the first letter of the colours given: R-135=3G+B and 33=4G+B. We want to eliminate B because the answer refers to green and red but not blue. So, rearrange the second equation to get B: B=33-4G.Then substitute this equation for B in the first equation to get: R-135=3G+33-4G, which can be manipulated to give R-135=33-4G. We want to make R the subject so rearrange: R=168-4G. But B=33-4G, so rearranging these both these equations so -4G is the subject and equating them gives: B-33=168-R. Using these equations, we know that R is greater than B.
Get answers quickly
Medicmind Tutor
Sun, 12 Jun 2022 09:11:12
We know smallest one is 1 and r must be the largest, either g or b could be 1. Sub g= 1 will not get the answer. Sub b =1, then 33= 4g -1, g=8. r then = 160. 160/8 = 20 = Ans B
At committee meetings of the Massing Social Club motions are carried or defeated by a simple majority, abstentions being ignored.
At the last meeting a proposal to install a satellite dish was defeated by 8 votes to 5 with 10 committee members abstaining. However, because of the large number of abstentions it was decided that the matter should be discussed further at the next meeting and a vote taken again.
Explanation
The correct answer is A.
If we want the minimum number of changes, ignore the abstentions and instead change as few people voting against the satellite dish to voting for. If you take 2 people from the 8 who voted against it would leave 6 voting against. If these 2 people then decided to vote for the satellite dish, you would get a total of 7 people voting for, which exceeds the 6 people who are now voting against. Hence the results have been reversed (the majority are now voting for) by 2 people changing their mind.
The United States Postal Service has an online guide to help people using their postal This is an extract:
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates – single piece rates
Parcels: Dimensions cannot exceed 1250 cm.
Letters: 30 cm long, 16 cm wide, 1 cm thick, maximum weight 360 grams. (Any item larger than this must be sent as a parcel).
I want to send two items through the post using first class mail. One is 50 cm long, 25 cm wide, 10 cm thick and weighs 300 grams. The other is 20 cm long, 12 cm wide, 0.20 cm thick and weighs 110 grams.
Explanation
The correct answer is C.
The first item is too large to be sent as a letter, so must be sent as a parcel. It weighs 300g, so it costs: 1.22+ (((300-30)/30)x0.17)=1.22+((270/30)x0.17)=1.22+(9×0.17)=2.75 dollars. The second item is small enough to be sent as a letter, but (110-30)/30=2.67 (not a whole number) so we must round this up to 3 (because 0.17 dollars is charged for each additional 30g or part thereof). So the second item would cost: 0.44+(3×0.17)=0.95 dollars. So in total the cost is: 2.75+0.95=3.70 dollars
The table below shows the energy values for the main foods used by volunteer wardens at a wild bird reserve to prepare a variety of feed mixes.
A trainee volunteer has been asked to prepare a sample of a special mix to provide exactly 5,000 calories. He has weighed out the first four ingredients but cannot read the required mass of the final ingredient because of an ink blot. This is what has been weighed out so far:
mealworms 150 g, apple 150 g, raisins 250 g, suet 125 g
Explanation
The correct answer is A.
First calculate the total number of calories in what has been weighed out so far: mealworms=1.5×150=225, apple=1.5×350=525, raisans=2.5×300=750, suet=1.25×800=1000. Add these together to calculate the total number of calories without the sunflower seeds: 225+525+750+1000=2500. We want to make 5000 calories, so we need the sunflower seeds to provide another 2500 (2500+2500=5000). Each 100g of sunflower seeds gives 500 calories, so we need 2500/500= 5 lots of 100g which is 500g of sunflower seeds.
The bar chart shows the amount of money in the savings accounts of three friends at the start of the year.
Since then, they have all spent the same amount of money from their accounts and the amount in Belinda’s account has halved.
Explanation
The correct answer is D.
Because they have all spent the same amount of money, the amount in their accounts in ascending order will remain Carol, Belinda, Arthur, so eliminate C because the section representing Carol is larger than that for Belinda. If you draw a horizontal line approximately half way up the bar chart representing Belinda, you can then slice the same amount off the other two bar charts by drawing horizontal lines through them. This will give you an idea of the relative sizes of the sections on the pie charts, which correspond to D.
The table shows the number of children in the town of Lancester aged 11 and 16 who play various sports after school.
Explanation
The correct answer is A.
Approximate the ratios by rounding each number to the nearest ten and then cancelling down as much as possible. Eg. for football 120:181 is roughly 120:180=12:18=2:3. The approximate ratios are as follows: swimming=2:3, footbal=2:3, cricket=12:13, hockey=5:6, tennis=4:5, squash=1:2.
Amy is researching her family She has two parents and four grandparents. However, she discovers that, among her great grandparents, two sisters from one family married two brothers from another.
Explanation
The correct answer is C.
The number of parents/grandparents doubles each generation – so you have 2 parents, 4 grandparents, 8 great grandparents and 16 great-great grandparents. However in Amy’s case since two of her great grandparents are sisters and two are brothers we’d be counted their parents (Amy’s great-great grandparents twice) and therefore we need to take away two lots of parents away to avoid this. This means that Amy has 16-(2×2) = 12 great-great grandparents and the correct answer option is C
The cost of entry to the Victoria and David Museum is as follows:
Adults £7
Children £4
Senior Citizens £5
This chart shows the breakdown of yesterday’s total takings of £679 by age group.
Explanation
The correct answer is B.
Divide the approximate takings for each age group by that age groups’ entry cost to calculate estimates for the number of visitors from each age group. Adults:400/7=57, children:150/4=37, seniors:150/5=30. Approximate total number of visitors=sum of approximate number of visitors from each age group=57+37+30=124. So the fractions for the pie chart would be: adults=57/124, children=37/124, seniors=30/124. Therefore on the pie chart, adults would make up less than half, children would make up slightly more than a quarter and seniors would make up slightly less than a quarter. These three conditions are only satisfied by pie chart B.
A public telephone has been vandalised and will take only 50 pence coins and 10 pence coins. A woman puts £8.50 into the phone to make a long-distance call with twenty-five coins. Five 10 pence coins are returned when she finishes her call.
Explanation
The correct answer is D.
You can form a pair of linear simultaneous equations. Let a be the number of 50ps the woman puts into the phone and let b be the number of 10ps the woman puts into the machine. 0.5a+0.1b=8.5 and a+b=25. Double the first equation and subtract this from the second equation, which gives 0.8b=8, so b=10. Substituting b=10 into the second equation gives a=25-10=15. Therefore the number of 50ps is 15 and the number of 10ps is 10. Subtract the five 10p coins the machine returns after her call to work out what the machine retains, which gives fifteen 50p coins and five 10p coins.
Nowadays many people in the UK work out their own income tax bills. Everyone has a personal allowance which is the amount of money they can earn each tax year before they start paying tax. Income above the personal allowance is taxed in bands. The UK tax bands and personal allowances for four tax years are shown below. The tax year runs from 6 April to 5 April the following year.
Mary is 52 and her husband is 58. Her only earnings each year are from a summer job. Between 6 April 2000 and 5 April 2001 she earned £5,585.
Explanation
The correct answer is B.
Mary is married and 52yrs old so will have a personal allowance of £4385. Subtracting these from her earnings: 5585-4385=£1200. This is below £1520 (the starting rate for 2000-01), so will be taxed at 10%, which is £120, which is answer B.
The graph below shows the cumulative rainfall for Malvern Wells in the UK for 2010.
Explanation
The correct answer is D.
Following the vertical line to the left of ‘Jun’ on the graph paper up to the graph gives a cumulative rainfall of approximately 170mm. Following the vertical line to the right of ‘Sep’ gives a cumulative rainfall of 400mm. To calculate the total rainfall within these 4 months: 400-170=230mm. To calculate the average monthly rainfall: 230/4=57.5mm/month which is very close to D. Using the precise reading for cumulative rainfall at the beginning of June which is 172mm, rather than the estimate of 170mm, and performing the same calculations described would give the correct answer of 57mm/month.
Duncan’s bath has a flat base and vertical sides. It can be filled completely from the hot tap in 15 minutes or from the cold tap in 10 minutes. Its capacity is 360 litres. When preparing a bath, Duncan’s habit is to run both taps together for 1½ minutes, before turning off the cold tap. He turns the hot tap off when the bath is ¾ full, then leaves the water for a while to cool down to a suitable temperature before he climbs in.
Explanation
The correct answer is B.
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Medicmind Tutor
Thu, 30 Jun 2022 14:49:46
Depth: 1sqare= 90L 4 square =360L but it said 3/4 full so only A B D are correct. Time : 1square = 1.5min . It takes 7.5. mins to full the tub with only hot tap so totally 5 square so and is B
anon
Medicmind Tutor
Tue, 03 Oct 2023 11:52:05
it takes 15 mins to fill the bath with hot? not 7.5
A film star has agreed to sign autographs for £1 each at a charity function, all day from 9 am to 6 pm.
He claims to sign his name consistently ten times every minute, but insists on having a ten-minute break after each full hour of signing.
Explanation
The correct answer is C.
First, calculate how long he actually spends signing. He will sign 9-10am, have a break until 10:10am, then sign from 10:10 until 11:10am, then have a break until 11:20am, etc. Time spent signing: 9-10am, 10:10-11:10am, 11:20-12:20, 12:30-1:30pm, 1;40:-2:40pm, 2:50-3:50pm, 4-5pm, 5:10-6pm. This gives 7 hours and 50 minutes spent signing in total, which equals 7×60+50=470 minutes. Multiplying this by 10 (because he signs ten times per minute) gives 4700 autographs. Each is sold for £1, so the autographs are expected to raise £4,700.
An examination contains five questions. Candidates are instructed to answer three questions only, including at least one of the first two and no more than one of the last two.
Explanation
The correct answer is C.
If the 5 questions were numbered in order of 1-5, the 7 possible combinations would be: 123, 125,135, 235, 135, 125, 235.
Deliveries of containers for a fast-food takeaway are made only four times per year, at the beginning of January, April, July and October. Last year the takeaway over-ordered containers and currently has 2,000 left. The number of containers used per month varies, but is no more than 3,000 and no fewer than 1,000. The maximum number that can be delivered at one time is 6,000. The usage for last year is illustrated below.
Explanation
The correct answer is A.
First, eliminate answers B and C because 7,000 are ordered in April, and the question states that ‘the maximum number that can be delivered at one time is 6,000’. Then, calculate the total usage for each quarter last year using values from the graph in thousands: 1st quarter=2+3+1=6, 2nd=3+2+2=7, 3rd=1+1+3=5, 4th=1+2+3=6. We can only order a maximum of 6 thousand, so we must keep 1000 spare to use in the second quarter in addition to ordering 6000. So we must order 5,000 in January (+the 2,000 we have already, which will give us 1,000 spare to use in the 2nd quarter), 6,000 in April (and we can use the spare 1,000 from the previous quarter to meet the total demand of 7,000 for this quarter), 5,000 in July, 6,000 in October.
An unusual dartboard is used in a playground game:
In order to win the big prize, contestants must score exactly 50 with three darts, all of which must be in different sectors.
Explanation
The correct answer is C.
Possible combinations include 18, 24, 28 and 18, 11, 21. The only number included in both of these is 18.
Fiona
Medicmind Tutor
Tue, 31 Oct 2023 07:01:21
18 + 24 + 8 = 50 18 + 11 + 21 = 50
Fiona
Medicmind Tutor
Tue, 31 Oct 2023 07:02:00
18 + 24 + 8 = 50; 8 + 11 + 21 = 50
The following is from a report on road accidents in Scotland in 1998:
A total of 13,828 car users were injured in road accidents, representing 62% of all casualties. Of these people, a total of 2,386 were either fatally or seriously injured, 223 of whom died. Roads in built-up areas accounted for a little over half of all car-user casualties (53%: 7,389 out of 13,828). Presumably because average speeds are higher in non-built-up areas, they accounted for much higher percentages of the total numbers of car users who were fatally injured (84%: 187 out of 223) or were fatally or seriously injured (72%: 1,724 out of 2,386).
Explanation
The correct answer is A.
This question provides a lot of information and unnecessary values to mislead you, hence it is key to quickly skim the paragraph, to look at what kind of information is being provided (e.g. total number injured, followed by statistics for roads in built up areas and then non built up areas), then look at what the question is asking and identify the key details to look out for (e.g. serious not fatal injuries in non-built up areas). From this we can tell that the information we require on non-built-up areas is at the end of the paragraph. Since 1724 individuals suffered fatal or serious injuries and 187 were fatally injured, we can do 1724-187 to calculate the answer. Clearly since the only answer option lower than 1724 is A, that must be the answer and we don’t need to spend time calculating the value accurately.
Last night I took part in a quiz night, and my team won first prize. The quiz consisted of three rounds:
Round 1 was 20 easy questions worth 1 point each;
Round 2 was 20 medium questions worth 2 points each;
Round 3 was 20 hard questions worth 5 points each.
Our winning score was 138 points, having answered just nine questions incorrectly.
The runners-up were annoyed because they had fewer incorrect answers, but fortunately for us (although a little embarrassing) we had more incorrect answers in Round 1 (the easy questions) than in either of the other two rounds.
Explanation
The correct answer is B.
The maximum points per round are Round1 = 20, Round 2 = 40 and Round 3 = 100. This gives an overall maximum of 160 points. Therefore, as the winning team got 138 points, this means that they were 22 points away from the maximum and this is due to the 9 questions they answered incorrectly. If we work through the answer options, for A we have to assume that they answer 4 questions wrong in round 1. This means that a. they got 5 questions wrong over rounds 2 and 3 and b. that in addition to the 4 points lost in round 1, they lost an additional 18 points over rounds 2 and 3. If we use trial and error at this point, we can see that this combination does not work as if we assume that they got 1 wrong in round 3, that means that they would get 4 wrong in round 2, which would be incorrect as they had more incorrect answers in Round 1 than in either of the other two rounds. If we assume 2 wrong in round 3, this still doesn’t work, as that means that they must have gotten the remaining 3 incorrect answers in round 2 but 2×5 + 3×2 = 16 rather than 18 and so on. So we can move onto option B. If we assume 5 wrong in round 1, that means 4 questions wrong plus 17 points lost over the remaining two rounds. Here, we can see that if we get 3 wrong in round 3 and 1 wrong in round 2 and that gives us 3×5 + 1×2 = 17, hence as this combination works, the correct answer is B.
A company is producing a one-page flysheet 24 cm high by 18 cm wide. It will have a text area in the centre which has a margin of the same width all the way around. The text must occupy exactly half of the total area:
Explanation
The correct answer is A.
Total area = 24×18. Area of the text area or the margin area (since it is split into two halves in terms of area) = (24×18)/2 = 216cm^2. If we work through the answer options, we can see that with a margin of 3cm, we would end up with (3×18)x2 = 108 for the top and bottom and for the two sides – (3x(24-6))x2 =108 so the margin area is 216cm i.e. half of the paper, which means that the text area occupies the remaining half. Hence, the answer must be A.
Daria and her three friends are planning a trip to London to see a musical in the West End. Ticket prices vary according to the location of seats in the theatre. Monday to Friday, Balcony seats are £78.20 per person; seats in the Dress Circle cost £95.50 per person; seats in the Grand Circle £88.99 per person; and seats in the Orchestra Stalls £82.00 per person.
At the weekend (Saturday and Sunday), Balcony seats are £81.35 per person, seats in the Dress Circle cost £99.99 per person; seats in the Grand Circle £93.20 per person; and seats in the Orchestra Stalls £86.00 per person.
The theatre also sells Boxes which seat four people and cost £320.00 in total. A special offer of 15% off group booking for four or more people is available on seats in the Dress Circle.
Explanation
The correct answer is A.
First, we can see that the box costs 320/4 = £80 per person. Therefore, we can rule out any option that costs greater than £80 straightaway. This means that we can rule out Grand Circle and Orchestra seats at any time of the week. We cannot rule out Dress Circle seats straight away because of the 15% discount, however we can also see that Balcony seats (£78.20 on weekdays) cost less than the box seat (£80) per person so the current lowest value seats are the balcony seats. When we consider the Dress circle seat discount, we can see that if we use the lower value Weekday price of £95.50, even then the 15% discount is unlikely to reduce the price to below £78.20 (to save time we can avoid actually calculating the value and simply estimate, i.e. if we round £95.50 to 100, then we can see that a 15% discount will reduce it to £85 nearly £8 more than the balcony tickets). Therefore the cheapest tickets are the Balcony seats, so the correct answer is A.
The payment systems which use pre-paid magnetic swipe cards are not all that wonderful. We had one put into the office last week to operate the tea and coffee dispensing machine. I was somewhat surprised to find, after having five coffees, that I had spent 121 p, and my colleague, after four teas, had spent 82 p. We were assured that there had been no changes in the prices; the problem appears to be that if you ask the machine how much you have left, it deducts a ‘service’ charge for this ‘service’. We both enquired once. Charges for tea, coffee and service are whole numbers.
Explanation
The correct answer is D.
This question can appear quite challenging if you try to work out the minimum costs purely on the basis of the following equations (where C= coffee, T= tea and S= service charge) 5C + S = 121p 4T + S = 82p However, it becomes much easier if you recognise that all you have to do is work through the answer options and take away the assumed service charge from both 121p and 82p and check whether the resulting value is still divisible by 5 and 4, respectively, because all the charges are whole numbers as stated in the question. If more than 1 option worked, then you would simply select the smallest value as we are told to calculate the minimum value that the service charge could be. Using this, we can work from A. 1p and we can see that while 121-1= 120 is still divisible by 5, 82-1= 81 is not divisible by 4 so A is incorrect. B. 2p: 121-2 = 119p which is not divisible by 5 so B is also incorrect, similarly C and E are also incorrect. If we check option D, we can see that 121-6 = 115 is divisible by 5 and 82-6 = 76 is also divisible by 4, so D is the correct answer.
Anna buys potatoes in the local market. She has noticed that the price on Saturday morning is 5 p per kilo more than the normal weekday price. However, an hour before the stall closes on a Saturday afternoon, the price drops to 5 p per kilo below the weekday price. She spends £3.00 a week on potatoes. This will buy her 3 kilos less in weight on a Saturday morning than on a weekday, but 5 kilos more in weight at the low Saturday afternoon price than on a weekday.
Explanation
The correct answer is C.
A café owner makes 50 mini pizzas and 50 flapjacks for sale during the day. The pizzas are sold for $2.00 each and the flapjacks are sold for $1.00 each. However, by the end of lunchtime there are 10 mini pizzas still unsold and 15 flapjacks unsold, so the price of each is halved for the afternoon. At the end of the day there are still 2 mini pizzas and 1 flapjack left which are given away free to the last customer.
Explanation
The correct answer is A.
Sales until lunchtime: 40 mini pizzas – 40 x $2 = $80; 35 flapjacks – 35 x $1 = $35; total = $80+$35=115. After lunchtime reductions: Pizzas – 8x $1 = $8; Flapjacks – 14 x $0.5 = $7; total = $15. Total sales – production costs = profit. So ($115+ $15) – $30 = $100
A picture 40 cm high by 30 cm wide is to be framed. There will be a mount between the edge of the picture and the frame. This mount will be 6 cm wide at the top and sides, and 9 cm wide at the bottom. The width of the wood used for the frame is 2 cm.
Explanation
The correct answer is D.
40 cm for the height of the picture itself + 6 cm for the mount above the picture + 9 for the mount below the picture, finally + 4 cm for the 2cm width frame above and below, giving us 40+6+9+4 = 59cm for the overall height
Tasty Crisps are currently running a promotion in which there is one money-off coupon inside every packet. Some coupons are worth 19p, some are worth 12p and others are worth 7p.
My friend tells me that he has at least one of each value and his seven coupons have a total value of exactly £1.
Explanation
The correct answer is C.
Since they have at least 1 of each coupon we can add up 19+12+7 = 38p. If we multiply this to get as close to £1 (after which point, we can slightly alter the number of each coupon to get exactly £1) we get 38 x 3 = 114p. This means that we can subtract 2 of the 3x 7p coupons to get the exact £1 total. As a result, we have 3x 19p coupons and therefore the answer is C.
I am planning to repaint the walls and the ceiling of my dining room. The room has the shape of a rectangular box and is 8 m long, 4m wide and 3 m high. I do not need to paint the door and the three windows, the combined surface area of which is 10 m². Paint is sold in 8-litre tins and 1 litre of paint is sufficient for a surface area of 12m².
Explanation
The correct answer is A.
The room is essentially a cuboid, so there will be two of each type of ‘face’. However, they are planning on painting the walls and the ceiling so remember to exclude the floor. As a result, the complete area of the room is given by 1(8×4) + 2(8×3) + 2(3×4) = 32 + 48 + 24 = 104m^2. Remember to take away the 10m^2 for the windows and doors which do not need to be painted, giving us a total area of 94. 12 goes into 94 more than 7 times but less than 8 times (7 remainder 10) so we need to round up to 8 litres. As paint is sold in 8 litre tins, 1 tin is sufficient. To save time in this question remember that we don’t need to accurately calculate 94/12 to the last decimal point as we will be rounding the value up at the end anyways. Also remember to read and underline key points in the question as you are reading so that you don’t forget to exclude the area for the floor, for example.
A laboratory technician has made up a stock mixture of two chemicals, X and Y, ready for use by all of the groups in Year 9 at a High School. He has mixed 6.0 kg which is ¼ of X and ¾ of Y. He realises that he has used the wrong mix and, rather than waste the chemicals he has used so far, he is going to add some more of chemical X so that the mix consists of 40% of X and 60% of Y.
Explanation
The correct answer is B.
Given that ¼ of the 6kg mix is X and ¾ is Y, this means that the mix consists of 1.5kg X and 4.5 kg of Y. as the technician will only add X to the mixture to correct the mix, this means that the amount of Y will remain unchanged. Hence 4.5kg of Y = 60% of the final mixture. As the ratio of the chemicals X and Y in the final mix is 40:60 which can be simplified to 2:3, we can work out the amount of X in the final mix with (4.5kg/3)x2 = 3kg. since we already have 1.5kg of X we need to add a further 1.5kg of the chemical, giving us the answer of B.
There are two ways of scoring points in a ball game: a ‘major’ scores 5 points and a ‘minor’ scores 3 points.
In a match played yesterday, the Reds beat the Blues 77–52 despite the fact that the Blues scored exactly twice as many majors as minors, whilst the Reds scored exactly half as many majors as minors.
Explanation
The correct answer is C.
Since the Blues score twice as many majors as minors, this translates into the following ratio 2(Major):1(Minor) = 2(5):1(3) = 10:3 which means that there are 13 ‘units’. If we divide their score of 52 by 13 we get 4 i.e. 4 lots of those 13 units. This gives us 4x 2(Majors): 4x 1(Minors) and therefore 4×2=8 majors for the Blues. For the reds the ratio is the inverse: 1(Major):2(Minor) = 1(5):2(3) = 5:6 = 11 units. 77/11=7 so we have 7x 1(Majors): 7x 2(Minors). So, they scored 7 majors. Overall, this gives us 8+7=15 majors in total, so the answer is C.
The following ingredient and nutrition information (rounded to the nearest 0.1 g or 1kcal) appears on a 300g packet of oatcakes.
Each oatcake provides:
Ingredients: oatmeal (77%), vegetable oils, wheat flour, sugar, salt, raising agent: sodium hydrogen carbonate.
Typical values per 100g: energy 1792kJ, 427kcal; protein 10.7g; carbohydrate 56.45g of which sugars 2.4g, starch 53.7g; fat 17.6g of which saturates 5.0g, mono-unsaturates 7.9g, polyunsaturates 4.5g; fibre 8.9g; salt 1.4g of which sodium 0.6g.
Explanation
The correct answer is D.
We’ve been given the nutritional information for 1 oatcake and the values per 100g, and we want to figure out the number of oatcakes in a 300g packet. Key fact to remember is that the values have been rounded slightly, which is more likely to affect the smaller quantities (e.g. 1.4g of salt) so it is better to use the larger quantities if possible. For example, looking at the energy in kcal, we can see that there are approx. 8 in 100g (427/53 = 8 remainder 3). The remainder is probably a result of the fact that the values have all been rounded slightly so we can easily ignore it. And this means that there are 8×3= 24 in a 300g packet. So the answer is D. if we use the other values to confirm this, we can see that you similarly get 24 for the fat, saturated fat and sugars, but you actually get 21 if you use the values for salt. As mentioned before, this is due to the effect of rounding as you can see that when you carry out 1.4/0.2 you get 7, implying 7 oatcakes in 100g, but actually if there are 8 oatcakes, then the salt per oatcake will be 1.4/8 = 0.175g, which would also get rounded up to 0.2 to the nearest 0.1g as well.
Joan has a cat called Tibber.
Every day Tibber is fed 2 sachets of wet food and 25 grams of dry food.
For some time, Joan has bought the cat food from the local pet shop where one box of 12 sachets costs £12.00 and one 400 gram packet of dry food costs £4.00.
Joan has now decided to buy all of the cat food from an online distributor.
Four boxes, each of 24 sachets of wet food, will cost £62.40, and one 2 kilogram packet of dry food will cost £16.00.
Explanation
The correct answer is B.
Costs (per day) using local pet shop:
Cost for two sachets of wet food: £12/6 = £2
Cost for 25 grams of dry food: 16 lots of 25 grams in a 400 gram packet, so the cost is £4/16=25p
Total= £2.25
Costs (per day) using online distributor:
Cost for two sachets of wet food: £62.40/4 = £15.60 per box and therefore £15.60/12= £1.30 for 2 sachets
Cost for 25 grams of dry food: 80 lots of 25 grams in a 2kg packet, so £16/80= 20p
Total= £1.50
Difference = 75p and the correct answer is B.
A particular computer game involves the capturing of three types of mythical creatures: Arps, Orps and Urps.
Arps have 6 legs, 3 horns and a tail.
Orps have 4 legs and 2 horns, but no tail.
Urps have 3 legs and a tail, but no horns.
The last time Billy played this game he captured 45 creatures with a total of 222 legs, 99 horns and 33 tails.
Explanation
The correct answer is A.
For these types of questions, you need to work through it step by step and identify the pieces of information that will be easiest to work with first. As a result, the first thing to notice is that only Arps and Urps have tails, and importantly they both have 1 tail each. This means that as we have 33 tails in total, the number of Arps and Urps added together will give us 33 as well. The only creatures remaining are the Orps, so if we take 33 away from the total number of creatures captured, we can calculate the number of Orps to be 45-33 = 12. Since only Arps and Orps have horns we can now calculate the number of Arps. The 12 Orps contribute 2×12 = 24 horns, so the remaining horns (99-24=75) belong to the Arps, which have 3 horns each. Hence, we have 75/3=25 Arps. Finally, now that we have calculated the number of Arps and Orps we can subtract it from the total number of creatures captured to find the number of Urps, 45-12-25=8. Hence the correct answer is A.
Each word in a word game is scored by adding up the values of its letters. Each letter has the same value whenever it appears but different letters have different values. I know the word values for TEAR, RITE, TREE and RAT, but none of the letter values.
Explanation
The correct answer is D.
Given that we know the word values for TEAR and RAT, we can subtract the value for RAT from TEAR to give us the letter value for E. We can then subtract the letter value of E from TREE twice, which gives us the value for T+R, which we can subtract from RAT to give us the letter value for A. We can also subtract the values for T+R and the letter value of E from RITE to calculate the letter value of I. Therefore, in total, we can calculate the letter values for E, A and I, so the answer is D.
There are 24 pupils in a class. They decided to help the local park by planting a total of 24 plants, a mixture of birch trees and roses. Each girl planted three roses, and every three boys planted one birch tree between them.
Explanation
The correct answer is D.
For this question we can start off assuming that for each girl planting 3 roses, there are 3 boys planting a tree. This gives us a ratio of 1 girl : 3 boys and 3 roses : 1 tree i.e. 4 ‘units’, and 24 (the number of trees and the number of students) is divisible by 4. If these numbers didn’t work, then in you would shift to perhaps considering other ratios such that 24 is still divisible by the number of ‘units’. However in this case, we can see that when we do 24/4 we get 6, which means (1×6) girls : (3×6) boys = 6 girls : 18 boys. We can see that these values add up to give us the right number of total students as well as plants. Now that we know that we are working with the right number of students, we can go back to the question itself and we can see that there are 18-6 = 12 more boys than there are girls so the answer is D
Jake has a 500 ml bottle of orange squash that he has made according to the instructions on the bottle of concentrate. The instructions dictate that he should add 4 parts water to 1 part concentrate. He accidentally spills his squash, and now there is only 400 ml in the bottle. He then tops up the remainder with concentrate.
Explanation
The correct answer is D.
After spilling his drink, Jake is left with 400ml of squash, but this is still in the ratio indicated in the instructions, i.e. 4 parts water to 1 part concentrate, which gives us a total of 5 parts. 400ml/5 = 80 and as we have only 1 part concentrate, this means that we have 1×80 = 80ml of concentrate within the 400ml of squash. As he then adds a further 100ml of concentrate to top up his 500ml bottle, so we end up with 80+100= 180ml of concentrate. As a percentage of the total that is 180/500= 36%.
The diagram below shows the method of construction of a book with four folded sheets in each block, and three blocks in total. Page one is the first page of the first block of four sheets. At the centre of each block, you can see the stitching that binds the book together.
A book is to be made using the same technique but with eight sheets of paper in each of the three blocks.
Explanation
The correct answer is C.
For this question remember to use the illustration provided for your benefit. We’ve been told that for the book being made there will be 8 sheets of pages being used as opposed to the 4 in the example illustration. From this we can work out that there will be 16 pages prior to the first centre of a block. This means that pages 16 and 17 will be in the centre of the first block, with the stitches visible. This isn’t provided in the answer options, so we need to work out the pages present at the centre of block 2. For this we need to add the pages within the first block + the first half of the second block (32+16=48). Hence pages 48 and 49 are in the centre of the second block and the answer is C.
Five girls are collecting shells on a beach. They are putting them in buckets that each hold 24 shells. At the end of the collecting time, they are going to ensure that they all have the same number of shells. Four of them are only two short of filling their bucket, but the youngest one is lagging behind with her total. Each of the others give her three shells from their buckets in order to equalise the numbers collected.
Explanation
The correct answer is B.
Since 4 of the girls are only 2 shells short of filling their bucket, this shows that they have 22 shells each. Each of the 4 elder girls then gives 3 shells to the youngest, which means that in the end each will end up with 22-3 =19 shells. As the youngest receives 3×4 =12 shells from the other girls, this means that she was 12 shells short of 19. Hence by herself she managed to collect 19-12 = 7 shells
Recently, packets of Amblers crisps have had ‘money-off’ coupons inside them. Some coupons are worth 9p, some are worth 14p and some are worth 20p.
George has been collecting these coupons. He has more 14p coupons than 9p coupons, and more 9p coupons than 20p coupons. The total value of all of his coupons is exactly £1.50.
Explanation
The correct answer is C.
You need at least one “20p” coupon and at least 2 “9p” coupons, adding those up we have 38p. Take that away from £1.50 we have £1.12 and divide that by 14p we have a perfect 8. 8+ 2+1 = 11 (option C)
Below is a greyscale image of the flag of Canada. The flag consists of two red strips on the left and the right, a white square in the middle, and a red maple leaf in the centre.
The width of the white square is twice as large as the width of a red strip. The red maple leaf occupies a quarter of the square in the middle.
Explanation
The correct answer is D.
Central white square is square so 2 x 2 = 4 (arbritary units). Each white stripe is 2 (height of square) x 1 (as given). We are told the leaf is 1/4 of the central square – if area of the square is 4, then the red leaf is 1, the rest of the white is 3. So adding up: two red stripes are 2 each + 1 from flag; white is 3 units. Therefore ratio is 5:3, option D.
The bar chart shows the total numbers of tickets sold for a concert over three nights.
Premium tickets are more expensive than Standard tickets.
Explanation
The correct answer is E.
We know that the premium ticket is more expensive then the standard one, but we don’t know how much more expensive it is. The first thing we can note is that when we compare sales between Thursday and Friday, we can see that more standart tickets were sold on Thurday (50 more tickets), at least 70 more premium tickets were sold on Friday – as premium tickets are more expensive, selling 70 more of them means that more money was made on Friday, regardless of 50 less standard tickets being sold. This means that answers A, C and D are incorrect as it is not possible for most tickets being sold on Tursday. Secondly, we must compare Friday and Saturday – while 100 premium tickets were sold on Friday, 150 more standard tickets were sold on Saturday – it is impossible to tell which day led to more profit as we do not know how much more expensive premium tickets are (for example, if they were 2x the price, more money would have been made on Friday – 100x2a = 200a, a being the price of standard ticket, which is more thatn 150a. Alternatively, if the price of the premium ticket is 1.2 times the price of the standard ticket, 100×1.2a = 120a which is less than 150). The answer is therefore E, as most profit was made either on Friday or Saturday.
Peter has drawn two diagrams showing information about the two cars owned by his parents:
Explanation
The correct answer is B.
Quickest way to approach this is to write out what each car is based on the graphs. Car 1 is older, cheaper, smaller and slower. Car 2 is newer, more expensive, bigger and faster. We are looking for the incorrect statement, which is statement B (“the cheaper car is bigger”) as car 1 is cheaper, but smaller. However if you have time it is worth checking through the other options in case you made an error from rushing.
Alex and Sue are playing a game with a set of nine cards, numbered from 1 to 9. A 3 × 3 grid of cards is dealt onto the table. The cards for the next round have just been dealt and are as shown below.
The first player chooses two cards and scores the difference between the two numbers. The second player then chooses two cards from the seven that are left and scores the average of the two numbers. The highest score wins the round. Both players must choose cards that are
either horizontally or vertically next to each other in the grid.
For this round of the game Alex has to decide whether to play first or second. She wants to make sure that she wins the round. If she has more than one possible winning move then she wants to achieve the highest score possible.
Explanation
The correct answer is E.
For this question we simply need to run through the answer options and rule out any option in which Alex will lose. With answer option A, we can see that if Alec selects 1 and 8, her score will be 7. If we simply scan the remaining cards and look for cards with a value greater than 7, we can see that 9 and 7 are next to each other, so if the second player selects these, their score will be 9+7/2 =8 which is greater than Alex’s score so we can rule out A. For B Alex gets a score of 6, but the second player can get a score of 6.5 by selecting 6 and 7. For C Alec gets a score of 1 and for D a score of 2 – neither will allow her to win. Having ruled out A, B, C and D, we can see that E must be the correct option. Timing Tip – always think about the most time efficient way of approaching a question, here, trying to work out the winning move based on the cards alone will take much longer than ruling out the answer options.
please help
Medicmind Tutor
Sat, 07 Oct 2023 22:02:53
for the arguement against A, it says choosing 9 and 7 would give the result of 8, but in the argument against D, it says it would give the result of 2??
Nathan is making a pair of trousers for his young son. The diagram shows the pattern for one piece. Four such pieces are needed.
For simplicity he assumes that he will need a 15cm × 38 cm rectangle for each piece. The material comes in three widths with prices as shown:
Material may be bought in lengths which are exact multiples of 10 cm.
Explanation
The correct answer is B.
Nathan needs four pieces. We can assume the cheapest way will be if he buys one large piece of fabric, that he later cuts into individual rectangles. Each of the four pieces will need to be 15 x 38, so either we can picture them lined up adjacent, for a total width of 60 (15×4) and height of 30, or we can picture them lined up on top of each other, for a width of 15cm and a height of 152 cm. Using the second measurement, we can treat the height as width by rotating the fabric, and will thus be purchasing from the 160cm width category. The price per metre is £2.80, we need 20cm as our height (technically only 15, but must be purchased in multiple of ten). 20 cm is 1/5 of a metre, so 1/5 x £2.80 = 56p. Therefore our answer is B.
The drawing below shows an allotment shed.
The four outside wood surfaces of the shed, including the door, need to be painted with three coats of paint. It takes 4 minutes to paint 1 square metre.
I have two identical sheds to paint and will take just one 20-minute tea break.
Explanation
The correct answer is E.
First we can work out the area being painted : the front and the back add up to (2.5 x 1) + (2 x 1) = 4.5m^2 and the two sides add up to (((2+2.5)/2) x1)x2 = 4.5m^2. This gives a total area of 9m^2. As takes it 4 minutes to paint, this will take: 9×4 = 36 mins and with 3 coats: 36 x 3= 108mins. Since there are two sheds, we can double the time, giving us 216 mins, and add the 20 min tea break, giving a total of 236 mins which is equal to 3 hours 56 mins, so the correct answer is E
Sourdough, an ingredient of many bread products, is a fermented mixture of flour and water. At 8:00 am on Monday morning, I start with a mixture of 50 g flour and 50 g water. Each morning at 8:00 am I double the weight of the sourdough by adding equal weights of flour and water.
I know that 1 g of the water content evaporates every hour. The bread recipe that I would like to use requires 500 g of sourdough. I also want at least 50 g of sourdough left over so that I can continue growing it for next week’s bread.
Explanation
The correct answer is D.
Do not forget water evaporating. We need a minimum of 550 grams on the day we select as the necessary amount of sourdough. At 8am on Monday, there is 100 g (50+50). By 8am Tuesday, 24g has evaporated as water. So we have 76g. We double this to give 152g. Wednesday 8am, another 24g has evaporated, so we have 128g. We double this to give 256 g. Thursday 8am, another 24g has evaporated, so we have 232g. We double this to give 464g. Friday morning, another 24g has evaporated, giving us 440 grams. We double this. We now have 880g, more than the minimum. It is Friday, so the answer is D.
A 250 g bag of mixed nuts lists the contents on the packet as follows:
As they are my favourite, I eat all the almonds in the packet and then re-weigh it. I find that the almond content was the minimum it could have been whilst being consistent with the labelling.
Explanation
The correct answer is C.
Since the almond content was the minimum it could have been whilst being consistent with the labelling, it must have been 20%. As the almonds have all been eaten this means that only 80% of the bag remains and since the peanuts can take up a maximum of 40% (of the original bag) we can see that they can take up a maximum of 50% of the bag now that the almonds have been removed. If this is difficult to see, we can calculate the actual mass – so we have 200g of nuts left and the maximum mass of peanuts is 100g, giving us the answer option of C
Official TSA Mathematical Questions (2008-2019) Review Screen
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Official TSA Mathematical Questions (2008-2019) Section
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Official TSA Mathematical Questions (2008-2019) Section
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