Official TSA Spatial Questions (2008-2019)

Explanation

The correct answer is A.

As in the bird’s eye view diagram the border around the smaller central square is continuous around the entire of the small square, it must be that each side of the sculpture is level when viewed on from any of the sides. Hence, A could not be a view from the side because a sqaure chunk has been removed. The remaining options are all possible.

Explanation

The correct answer is B.

Pattern B can not be made using only the tile shown. This can be seen by looking at the leftmost tile in the 2nd row of pattern B (for example), which shows two curved black lines arching over opposite corners, whilst the tile shown in the question has a curved black line in only one of the corners and a more square black line in the opposite corner (rather than another curved black line). Therefore, B uses a tile other than the one given in the question. All the other patterns use only the tile given in the question.

Explanation

The correct answer is D.

Vinod can see a stack of 3 boxes in the leftmost column that he can see. The bird’s eye view from above shows that this leftmost column from Vinod’s view consists of a single stack of boxes. This means that that stack is exactly three boxes tall and therefore any of the answer options in which the middle column from Sarah’s view is less than 3 boxes tall cannot be possible. This means that answer option D is not possible and therefore that is the answer.

Explanation

The correct answer is D.

A can easily be made by moving the inferior points of the two side tables towards the centre until they touch. B can be made by rotating the left side table so that its largest side is against the largest side of the table in the middle and rotating the table on the right side so that its most superior (diagonal) side is against the right side of the middle table. C can be made by rotating the table on the left side 180 degrees clockwise and rotating the table on the right side 180 degrees anticlockwise. E can be made by rotating the table on the right side so that its largest side is against the largest side of the middle table and rotating the left table 45 degrees anticlockwise. Therefore the only shape that cannot be made must be D.

Explanation

The correct answer is D.

Nickel is 28km from Gold, so Nickel must be at a dot which has a line representing 28km attached to it. This could be P, Q, W, V, S or T, but since P and V are not given as answer options these can be eliminated, so Nickel could be Q, W, S or T. The next closest town to Nickel is lead, and since there are no lines representing 40km, this must be made up of 2 or more lines. We need to find which of Q, W, S and T are joined to 2 or more lines which add up to 40km. Q is not, W is (W to S=28+12=40), S is (S to W=12+28=40), T is (T to V=28+12=40), so eliminate Q. The next closest town to Nickel is Tin 63km away, using a similar method as we did for 40km: W is not joined to any number of lines equating to 63km, nor is S, but T is (S to T to V to U =28+12+23=63). Therefore Nickel must be T

Explanation

The correct answer is C.

Each diagram has 4 dots connected to 3 other dots and has 2 dots connected to 2 other dots, except C, which has 5 dots connected to 3 other dots and only 1 dot connected to 2 other dots. Therefore the connections on C are different to on all the other diagrams, so C is the answer.

Explanation

The correct answer is C.

We need to find the repeating unit that would make up this pattern with no overlap of tiles. Such repeating unit can be demarcated by counting 6 triangles down from the top left corner, 6 triangles along the top (diagonal) row, then the triangles on the left of the vertical line level with the right edge of the upper left hexagon above the northeast edge of the hexagon, then the remaining triangle above the line level with the northeast edge of the hexagon (against the hexagon’s northwest edge). This would give a total of 12 triangles for 1 hexagon.

Explanation

The correct answer is E.

Explanation

The correct answer is A.

Explanation

The correct answer is C.

Explanation

The correct answer is C.

From the view when looking that the books in the book shelf straight on, we can only determine the relative heights of the books, but not their widths. Hence when we look at them from the left, we can determine which of the views are possible on the basis of the different heights, but not the widths. From the view straight on, we can see that we should be able to see the top edges of at least 4 books, (highlighted in blue) simply because each one is taller than the previous ones. Therefore, any answer options where we can see these 4 books of different heights on the leftmost edge of the view is possible, as shown for options A and B. However, in answer option C, we only see 3 books on the leftmost edge, and therefore this is not a possible view.

Explanation

The correct answer is B.

A is the view from the right side, C from the bottom, D from the top and E from the left. Therefore B is the answer.

Explanation

The correct answer is B.

This questions requires that you visualise the two squares in different arrangements that produce the overlaps shown in the answer options. It is useful to look out for parallel sides and 90-degree angles in the overlapping shape as those can help indicate the placement of the two transparent squares. As shown, answer options A, C, D and E are all possible, and therefore the correct answer is option B.

Explanation

The correct answer is C.

C is the answer because if the opponent puts either an ‘X’ or and ‘O’ in any of the remaining squares, the player will be able to form a line of 3 identical symbols and therefore win.

Explanation

The correct answer is E.

A is possible as the rectangular face shown in A is the rectangle at the top of the card in the diagram given in the question and is adjacent to the triangle on the right hand side of the diagram. B similarly shows the rectangular face at the bottom of the diagram. C shows the middle rectangular face, and the triangular face on the right hand side of the diagram in the question. D is like A but includes the triangular face on the left of the diagram (rather than the one on the right shown in A). Therefore E must not be possible.

Explanation

The correct answer is D.

If we give each triangle a name: The top triangle is triangle 1, the two triangles below are L and R triangle 2 and the two triangles at the bottom are L and R triangle 3. There are 5 separate triangles in total, each of which touch the intersection, therefore each is a different possible path that could be taken, giving 5 possible paths so far. Now we need to find triangular paths that can be made by joining two or more triangles together. The following combinations of triangles are possible: 1+L2, 1+R2, L2+L3, R2+R3, L2+L3+R3, R2+R3+L3, giving us 6 more possible paths. So the total number of possible paths are: 5+6=11.

Explanation

The correct answer is C.

A could be the view of the third cylinder in the picture from the side if the cylinder was cutr longitudinally. B could be the view from any of the three cylinder from above if the cylinder was cut transversly. D could be the view of any of the cylinders from above when cut longitudinally. E could be the side view of one of the cylinders when cut diagonally. Therefore C is the answer.

Explanation

The correct answer is B.

Rotating B 180 degrees would mean the hexagon is in the bottom right corner, the rectangle is in the leftmost square of the 2nd row and the remaining shapes could be covered by circles to give the layout of the board above.

Explanation

The correct answer is A.

The quickest approach to answering this question is to simply run through the different answer options and see if they meet the requirements. As we start off with A we can see that it meets the distance limits of both Gordon and Helen. However, it is not instantly clear at first glance whether or not this lies within the distance range indicated from Ingrid’s location. As 22,07 is the point diagonally across from Ingrid it will be more than 1000m away from Ingrid but it is less clear whether it is further than 1100m away. Hence, we can go through the remaining options to check whether all the rest can be excluded. B and C can be excluded as they are clearly more than 1800m away from Ingrid. D is further than 2000m away from Gordon, while E lies 1000m away from Ingrid even through the signal strength suggests that the falcon is at least more than 1100m away. So, A must be correct. An alternative approach may be to annotate the image with circles indicating the different signal ranges provided but this will only take you longer to answer the question.

Explanation

The correct answer is A.

A is the answer as when the paper in A is folded along the dotted line, the hole in the shape will remain the same (no parts of the paper on one side of the fold will overlap parts of the hole on the other side of the fold).

Explanation

The correct answer is A.

The shape given in A can fit into the leftmost part of the trapezium, keeping A in the same orientation in which it is shown. If we then rotate shape A 180 degrees, it can fit against the vertical side of the first of shape A that we fitted into the trapezium. Keeping shape A in the orientation in which it is given, we could then fit it so its longest (diagonal) side fits against the longest side of the second shape A we used. Finally, flipping a fourth of shape A in the vertical plane would allow it to fit into the rightmost part of the trapezium.

Explanation

The correct answer is C.

All the shapes have the same L shaped ‘backbone’ and it is therefore easier to compare similarities and differences by focusing upon the 2 cube protrusions from this ‘backbone’. In doing so we can see that shapes B and E are the same and the protrusions here extend out in opposite directions while A and D are also the same. The only shape that is different to all the others is therefore C. It can be tempting to interpret the question to mean that 4 of the shapes are the exact same with one odd one out, which can become confusing when trying to answer the question. Since the question is only asking for one shape that is ‘different from all the others’, this doesn’t necessarily mean that the other four shapes are identical – just that there is at least one other shape that is identical to it.

Explanation

The correct answer is E.

We need to see which of these shapes can be made by visually attempting to fit 4 tables into it, or by drawing lines on the shapes to show separation of the tables. For shape A, the 1st table in the orientation shown in the diagram can fit into the top left corner of the shape, and rotating the 2nd table by 90 degrees clockwise, would allow it to fit on the bottom left corner; the same can be achieved with two consecutive rotates of 90 which would allow the table to fit into the bottom right and then the top right corner. Shape B can be made by fitting one table into each of the top corners, and then making the remaining rectangles by taking the table in the orientation given, rotating another table by 180 degrees and fitting these together. Shape

Explanation

The correct answer is E.

A can be done by drawing a horizontal line between the upper 2 corner (below the apex). B can be done by drawing a line from the middle of the left diagonal edge to the upper right corner or from the middle of the right diagonal edge to the upper left corner. C can be done by drawing a line from the left vertical edge to the base or the right vertical edge to the base. D can be done by drawing a horizontal line between the middle of the left and right vertical edges.

Explanation

The correct answer is E.

A and B are not correct because they contradict the description that only doors are on the westernmost end of the church. C is incorrect because the description states that there are 3 south-facing windows, whereas in the picture there are only 2. D is incorrect because when viewing from the South the longer horizontal part of the church would be on the left, like in diagram C. Therefore E is the correct answer.

Explanation

The correct answer is B.

A is the view facing the face on bottom of the diagram given, C is the top face, D is the right face and E is the bottom face again (as the weight can be either side up). So B is not a side view.

Explanation

The correct answer is E.

The 4th and 8th symbols are the same, suggesting that the 4th and 8th letters of the word must be the same. The only word given that has this is ‘sometime’, therefore E is the correct answer. You may have incorrectly thought that the answer was ‘saturday’ because the downward pointing arrow represents letter ‘A’ in the example given when Alistar’s name is written, however the text states that any particular symbol does not necessarily stand for the same letter of the alphabet each time, and the 4th and 8th letters are not the same in ‘saturday’.

Explanation

The correct answer is B.

Explanation

The correct answer is D.

D is not possible because the black rectangle in the bottom left corner of the remote (when viewing from the position of the arrow) would correspond to the leftmost block on diagram D. However, on diagram D this block overlaps the second block to the left in the row of blocks behind the two black blocks, whereas in the diagram of the remote the length of the bottom left black block does not extend for enough into the middle of the remote to cover the gap between the first and second blocks in the row behind.

Explanation

The correct answer is E.

If we imagine that we are taking the pictures as we move from right to left in field Y, we can see that in the initial pictures the order will be 1-2-4-3, followed by 1-4-2-3. Right in the middle of field Y, if pictures are taken from close up then the order will appear to be 1-4-3-2. As we continue onto the left side of the field the order will initially appear to be 4-1-3-2 and then 4-3-1-2. This means that 5 different orders are possible and the correct answer is therefore E.

Explanation

The correct answer is B.

A can replace the third tile on the bottom row when rotated 90 degrees clockwise. C can be rotated 90 degrees to replace the central tile for the letter S. D can replace the first tile of the second row when rotated 90 degrees anticlockwise. E can replace the first tile of the bottom row when rotated 180 degrees. This leaves B, which is the mirror image of D but the two are non-superimposable.

Explanation

The correct answer is E.

We can see that the leftmost stack of cubes only consists of 1 cube, allowing us to rule out options B and D. The next stack (moving to the right from the leftmost stack) contain two cubes, so we can rule out C. We are left with options A and E, and since there are two cubes in the rightmost stack, the correct answer must be E.

Explanation

The correct answer is A.

We can see that the only possible combination that uses 4 of the shapes and gives a shape that is twice as long as it is wide uses shapes W,X,Y and Z, so the answer is A.

Explanation

The correct answer is D.

For diagram A, height would initially increase with time at a constant rate, then at a faster rate when it gets to the open trapezium-like shape, from when the rate of height increase with time will decrease, ending at the original rate, which is shown by the second graph. For diagram B, the rate of increase in height would initially decrease at it gets to the centre of the circle, then the rate would increase until it gets to the two vertical lines, when it’s rate of increase in height with time would be at it’s highest and would remain constant, which is shown by the fourth graph. For C, the rate of increase in height would remain constant throughout, which is shown by the first graph. For E, the rate would initially be constant, before instantaneously switching to a higher rate, shown by the third graph. For D, the rate would for the most part be constant, then increase, before again remaining constant but at a higher rate, which is not shown by any of the graphs.

Explanation

The correct answer is A.

Adding another square border of dots around the 36 mushrooms adds 2 mushrooms to each row, making the total square 8x8m (64 mushrooms). So the number of mushrooms ascends every other square number (2×2=4, 4×4=16, 6×6=36, 8×8=64, etc.). Because the field is 100x100m, and the number of mushrooms in each row increases by 2 each day, to find the answer: 100/2=50 days to fill the whole field from the very start. Because the mushrooms started to grow 2 days ago, subtract 2: 50-2= 48 days.

Explanation

The correct answer is C.

Explanation

The correct answer is A.

Remember to take note of the fact that the tiles are shown face up and cannot be laid face down – so although you can rotate the shapes you cannot turn them over. Just a quick scan of the shapes shows us that shapes 1 and 2 pair well with each other but not with the other shapes as 2 has a protrusion in the centre, which tile 1 can accommodate unlike the other shapes. Therefore, any combinations with just 1 or just 2 are less likely to work. This alone allows us to rule out options B-E. However, it is important to still confirm this by attempting to visualise whether tiles 1,2 and 5 fit together to form the L shaped area and we can see that they do, leaving us with A as the correct answer.

Explanation

The correct answer is E.

To answer this question we need to compare two grids at a time. If the grids differ by 1 square only, then it is possible that one of them is correct and if they differ by more than one square, then neither are correct. The correct grid will differ from each of the other grids by only one square. Hence if we compare A with C we can see that they differ by 2 squares – so neither can be correct. Same is true for when we compare B and C as well as D and C. so we can rule out options A, B, C and D, giving us the right answer of E. Just to confirm, we can check and see that E only differs by 1 square when compared to each of the others, hence it’s the correct grid

Explanation

The correct answer is C.

If you draw the token and turn it 180 degrees the token you draw should fit into the original one in the option. C doesn’t fit therefore its the correct option.

Explanation

The correct answer is A.

Net A cannot form the L-shaped box because if you, for example, fold along the left and right vertical dotted lines so the two L-shaped faces are parallel to each other, the upper left square on the diagram of the net would overlap with the lower part of the L-shaped face on the right in the net diagram. This would leave a gap in the position of the lower square face (the rightmost square face in the diagram of the box given in the question). All the other nets will from the box when folded.

Explanation

The correct answer is D.

D is an impossible arrangement as for this to possible, one of the tables would have to be turned upside down. All other combinations are possible by moving the tables (upright) around into different positions.

Explanation

The correct answer is E.

The answer is E , as from Amy’s view, you can see that the second pile from the right appears 7 boxes tall. This means that at least one of the piles coloured in green must be 7 boxes tall and as a result, at least one of the two rightmost piles must be 7 boxes tall in Ben’s view. This is true in all answer options except for E, so that is the correct answer. Top Tip: For these kinds of questions, as you usually only have to figure out which of the views is not possible, make sure to start off with the piles that are easiest to work out, such as the leftmost pile from Amy’s view, as from the bird’s eye view we can tell that it’s only one pile and therefore it must be 5 boxes tall – and therefore the second pile from the left in Ben’s view must be atleast 5 boxes tall.

Explanation

The correct answer is E.

This question requires you to visualise the shapes provided and see which of the answer options could not be made from the two pieces. Make sure to draw on the shapes to figure out whether or not the combination is possible. From this we can see that answer options A-D are all possible and the correct answer is E.

Explanation

The correct answer is B.

Although this question can look quite difficult at first due to the amount of information provided, it is pretty straightforward once you understand how the grid references work. We can see some points are present at either extremes within the grid (both along the vertical and horizontal axis). Use these to label your axis. Along the horizontal axis, we can see a point at the left most extreme and scanning the grid references shows that the place with the highest number for the horizontal aspect is Lower Green, with 837654. If we label our horizontal axis accordingly, and note the fact that the grid reference for Long wood is 787634, we can see that the two points within the 78-79 square (horizontally) are W and Y. Between these, we can see that W is the correct answer as its most likely to be 787… whereas Y likely has a grid reference of 781… (which is Riverside).

Explanation

The correct answer is C.

All options aside from C are anti symmetric, where the right side is the opposite of the left side. Therefore, they become symmetric about a vertical axis when one side is reversed.

Option C is already symmetric, meaning that it will become anti symmetric when one side is reversed.

Explanation

The correct answer is E.

We are looking for the impossible view; E is not possible because the indent in the rectangle is not closed at all in the 3D shape, so there would not be a line across the rectangle as is shown in E (birds eye view from above)

Explanation

The correct answer is C.

This is a little time-consuming. I would recommend sketching out the digital display. Then above/next/beside each line segment, write which numbers between 1 and 9 would light up that segment. Each, the number 8 would light all of them, or the uppermost bar would be let by 2,3,5,6,7,8,9. The lower right hand bar is let by the numbers 1,3,4,5,6,7,8,9 which is eight, the maximum. The minimum is the lower left bar, which is only lit by the numbers 2,6,8, so three is the minimum, and the answer is C.

Explanation

The correct answer is C.

For these kinds of net questions, try to find an easy pattern than you can look for within each net to rule out the incorrect ones. For example, here, we can observe where the top of the letter T on the hexagonal face lies. We can see that it faces a corner, so we can instantly rule out answer option B as the top of the letter T lines up with a side in option B. We can also see that the top of the letter T lies near the corner with the numbers 2 and 3 making up the sides of the prism. Scanning through the remaining nets allows us to rule out A and E, as the top of the letter T lies near the corner with the numbers 1 and 2 making up the sides instead. For D its 3 and 4 so it can also be ruled out. This gives us the correct answer option of C. If visualising this proves to be hard, it is also worth looking at the order of the numbers on the sides of the prism – this allows us to rule out D for instance, while we can rule out A and E because all the numbers are oriented sideways – so the wrong way round.