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Emmaline is deciding whether to buy a gym membership from Gym A or from Gym B.  Both gyms are open 7 days of the week.  Gym A has free equipment 6 out of 7 days of the week, and Gym B has free equipment 80% of the time.  Gym A has personal trainers 5 days of the week, and Gym B does not have personal trainers 8/28 of the time.

Q1 Considering only the availability of equipment and presence of personal trainers, should Emmaline get a gym membership at Gym A?
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## Explanation

The correct answer is AJot the information that you know into a table using the ‘same, simple, positive’ rule.  Keep the information in the same and most simple format, looking at the information the question is asking about.  The question asks us to consider only availability of equipment and presence of personal trainers.  Note that for Gym B, we are told the probability of personal trainers not being there, so to find the probability of personal trainers being there, subtract this from 1.

 Gym A Gym B P(equipment available) = 6/7 = 0.857 P(equipment available) = 0.80 P(personal trainers available) = 5/7 P(personal trainers available) = 20/28 = 5/7

Both gyms have the same presence of personal trainers, but Gym A has more free equipment than Gym B, so A is the correct answer.  B, and D are incorrect because there is equal personal trainer time at both gyms; C is incorrect because the answer choice says that Emmaline should not get a gym membership at Gym A, though she should, based on the equipment availability.

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All waitstaff at a restaurant must wear black. Some waitstaff at this restaurant tie their hair back.Some people work part-time at the restaurant. All part-time waitstaff at the restaurant walk to work.

Q2 Place ‘Yes’ if the conclusion follows. Place ‘No’ if the conclusion does not follow.
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## Explanation

Some waitstaff do not walk to work.

o   No.  We are told all part-time waitstaff walk to work.  We cannot conclude that others do not walk to work.

If a person works at this restaurant, they are wearing black.

o   No.  We are told that waitstaff wear black, but there may be other people working at the restaurant that are not waitstaff, and these people may not have to wear black.

There are full-time and part-time waitstaff at the restaurant.

o   No.  We are not told anything about waitstaff working full-time.  We know some waitstaff work part-time, however we do not know if any waitstaff work full-time.

If a waiter works part-time, he must walk to work.

o   Yes.  We are told that all part-time waitstaff at the restaurant work to work.  If a waiter works part-time, he must walk to work.  This conclusion follows.

It is possible for a waitress at the restaurant to wear black, tie her hair back, work part-time, and walk to work.

o   Yes.  All waitstaff wear black.  All part-time waitstaff walk to work.  Some waitstaff tie their hair back.  So, it is possible for a waitress to wear black, work part-time, walk to work, and tie her hair back.

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Helen Medicmind Tutor

Sat, 22 Aug 2020 13:15:23

This question type does not work as it does in the UCAT mock tests, with the dragging options :(

bob Medicmind Tutor

Sun, 04 Oct 2020 07:55:25

"If a waiter works part-time, he must walk to work" is false as it never states that the waiter works for this restaurant, but the question specifies that "All part-time waitstaff at the restaurant walk to work". This whole test is fairly poorly written.

Should secondary schools be open 6 days a week instead of 5, so that students can learn more content faster and be better prepared for exams?

Q3
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## Explanation

The correct answer is CThe key bit of information in this question is ‘learn more content faster and be better prepared for exams.’  We want to know if having a 6-day week will contribute to this, and the arguments represented in an answer choice should relate directly to this in order to be strong.   A and B do not discuss exam preparation or learning content, so are not relevant enough to the question, and are therefore incorrect.  D might seem like a promising argument but does not have any research basis and is a bit speculative, so C is a stronger answer.  This answer choice both addresses exam preparation and learning content and mentions that there is research to back up this claim.

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Kendrick and Kiara often wear floral tops to university.  There is a 20% chance Kendrick will wear a floral top, and a 1/4 chance that Kiara will wear a floral top.

Q4. Is there a greater than 50% chance that at least one of them will wear a floral top to university?
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## Explanation

The answer is C. To work out the probability of at least one of them wearing a floral top, calculate the probability of neither wearing a floral top and subtract this from 1.  The probability of Kendrick not wearing a floral top is 0.80 and the probability of Kiara not wearing a floral top is 0.75.  The probability of neither of them wearing a floral top is 0.80 x 0.75; 1 – (0.80 x 0.75) = 0.40 (because P(not A) and P(not B) = P(not A) x P(not B)). This is not greater than 50% (0.50), so the answer is No, C.

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Albie is baking peanut butter cookies for his friend’s birthday.  The recipe calls for 200 g of peanut butter, 175 g of golden caster sugar, ¼ tsp fine salt, and 1 large egg in order to make 16 cookies.  At home, Albie has ½ kg of peanut butter, 355 g of golden caster sugar, 80 tsp of fine salt, and 4 large eggs.

Q5. Does Albie have enough ingredients to make 2 batches of cookies?
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## Explanation

The correct answer is C. In order to make 2 batches of cookies, multiply the recipe values by 2.  Albie would therefore need 400 g of peanut butter, 350 g golden caster sugar, ½ tsp fine salt, and 2 large eggs.  Albie currently has ½ kg (500 g) of peanut butter, 355 g golden caster sugar, 80 tsp fine salt, and 4 large eggs, so this is just sufficient to make 2 batches of cookies.  He could not make an additional batch because he does not have sufficient golden caster sugar or peanut butter to do so.  Be mindful of units (for peanut butter).

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Children in a class have a variety of different fruits for snack time. Some children have apples. Some children have strawberries. Some children have blueberries. All children that have blueberries also have strawberries. Some children have all three fruits.

Q6 Which one of the following diagrams best represents the above information?
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## Explanation

The correct answer is A. There are three fruits, each represented by a circle. Because we are told that some children have all three fruits, the answer cannot be C or D, as there is no region which accounts for the three circles overlapping.  We are also told that all children that have blueberries have strawberries, which means we need to find a circle that sits completely inside of another circle, which is the case for answer choice A, and not answer choice B.

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Five friends, Zahra, Marianne, Layla, Sophie, and Jade are planning what to wear to the school dance.  Each friend wears a different coloured gown, and no two friends wear the same shoe.  They wear gowns coloured red, navy, black, gold, and white.  Their shoes are black heels, black flats, red heels, gold heels, and nude flats.

Sophie and Zahra both wear black shoes.

Jade and Zahra both wear flats, whilst the rest of the girls wear heels.

Marianne wears red heels and a black gown.

Only Layla wears a gown and shoes of the same colour.

Q7 Which of the following must be true?
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## Explanation

The correct answer is B.  Begin slotting information into a table based on the points provided.

 Shoe Gown Zahra Black heels Marianne Red heels Black Layla Gold heels Gold Sophie Black flats Jade Nude flats

The only one of the answer choices that can be concluded with certainty from the given information is B.  The others are all possible, but not certain.

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zohra Medicmind Tutor

Sat, 29 Aug 2020 11:12:46

in the question it says zahra wears black and flat, but in the answeer it is says zahra wears black high hells

The following information is given for Year 12 students at a school.  Students can take one or two languages.

20 people study Spanish.

40 people study French.

15 people study German.

No one studies both German and Spanish.

6 students study exactly two languages.

Twice the number of students that study French and German study French and Spanish.

Q8 How many students study German only?
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## Explanation

The correct answer is C We are told that the number of students taking French and Spanish (p) is twice the number of students taking French and German (q).  So p = 2q.  We also know that 6 students take 2 languages and the only combinations of these are French & German or Spanish & French (no students take German & Spanish).  So, p + q = 6.  Substituting p = 2q into the above equation, we get 2q + q = 6, so 3q = 6.  From this, we can deduce that q = 2.  So, 2 people take French & German.  The number of people taking German overall is 15, so the number of people taking only German is 15 – 2 = 13.

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At a particular office, cubicles are aligned in rows of six.  Colleagues Abi, Benji, Chloe, Deirdre, Esteban, and Flora sit in cubicles in one row of the office.

Abi sits next to only one other person, Esteban.

Exactly two people sit in between Benji and Chloe.

Esteban and Chloe sit equidistant from Deirdre.

Q9 Which of the following could represent the arrangement of the office cubicles?
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## Explanation

B is the correct answer. From the first point, we know that Abi must sit at the end, because he sits next to only one other person.  We also know that Abi sits beside Esteban from this point.  This eliminates answer choice D.  Because we know where Abi and Esteban sit, choose the next statement that talks about the relation between others and either Abi or Esteban.  Point three tells us that Esteban and Chloe sit equidistant from Deirdre, which means that Deirdre sits in between Esteban and Chloe, which eliminates answer choice D.  If Deirdre were directly next to Esteban, Chloe would have to be directly next to Deirdre (they sit equidistant from Deirdre), Flora would have to sit directly next to Chloe (Flora sits adjacent to Chloe), and Benji would be at the end.  This correlates to answer choice A, but does not account for two people sitting in between Benji and Chloe (there is only one, Flora).  This eliminates answer choice A.  B is correct because it is the only seating combination that satisfies all of the given information.

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