GATE CS 2022 Set 1 — Question 5
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General Aptitude → Spatial Aptitude → Transformation of Shapes (Translation, Rotation, Scaling, Mirroring)
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Question
A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.
From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.
Correct answer
(B) [figure]
Solution
The player starts with letters A and D.
To form a 5-letter palindrome, the set of 5 letters must consist of two pairs of matching letters and one central letter (e.g., ).Let's analyze the options (allowing for rotation):
To form a 5-letter palindrome, the set of 5 letters must consist of two pairs of matching letters and one central letter (e.g., ).Let's analyze the options (allowing for rotation):
- Option (A): Contains D, O/Q, J. Total set: {A, D, D, O, J}. We have a pair of Ds, but A, O, J are singles. Cannot form a palindrome.
- Option (B): Contains R, an inverted 'A' (which becomes A when rotated), and a rotated 'R' (which becomes R). Total set: {A, D, R, A, R}. This gives us two As, two Rs, and one D. We can arrange these as R A D A R, which is a palindrome.
- Option (C): Contains Z, 3, D. Total set: {A, D, Z, 3, D}. Pair of Ds, but A, Z, 3 are singles. Cannot form a palindrome.
- Option (D): Contains I, 7, Y. Total set: {A, D, I, 7, Y}. All singles. Cannot form a palindrome.
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