Question

A number of blocks are provided and they need to be arranged in the shape of a big square.
Which of the following blocks fits into the big square by just following translation?

• A. Q
• B. U
• C. V
• D. T

Answer 1

The correct option is A Q

Let’s analyze each of the rectangular blocks to figure out which block in the first image was placed in the second image. From the given blocks, we have only one that undergoes a translation and the remaining goes through rotation. In the second image, we are only given the height of some of the blocks. The height of the others can be derived from it.

$\bullet$ From the given blocks, the only one block which has a side of 35 units is P. But it’s not the height, so P was rotated by ${90}^{\circ }$. This block is numbered 1.
$\bullet$ The only block that has a dimension of 45 units is T. T’s width is the same as the height of one of the blocks. So, T was rotated to get the block numbered 2.
$\bullet$ Block 3 with a height of 15 units can only be V whose width matches. So, V was also rotated.
$\bullet$ Block 4 with a height of 40 units matches with the width of U. So, U was also rotated.
$\bullet$ Block 7 has a height of 25 units.
(The figure is a square so it’ll have equal sides.
$\Rightarrow$ 35 units + 45 units = Height of block 7 + 40 units + 15 units
$\Rightarrow$ Height of block 7 =
35 + 45 - 15 - 40 = 25 units
The only block that has a dimension of 25 units is block Q whose height is also 25 units. So, block Q matches 7 and it is not rotated unlike the others.

So, among the blocks given in the options, T, U, and V have to be turned, or in other words, undergo rotation before they fit into the big square. Only the block labeled Q does not require any turn or rotation and would fit right into the big square by following translation.