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: Plate 1: A Plate 2: D 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 five plates exactly once. The plates can be rotated in their plane. A. Q I Z B. D I A C. M I W D. I I Z
GATE 2022 · General Aptitude · Image Rotation · medium
Answer: Option B (plates D, I, A) — the five plates spell A-D-I-D-A, a valid 5-letter palindrome.
- Identify palindrome requirements for 5 letters: We need exactly two matched pairs of letters plus one singleton (middle). The two given plates supply A and D. We need the 3 additional plates to complete two pairs and provide a middle letter.
- Check Option A: plates Q, I, Z: No two letters match, so no palindrome arrangement exists. Eliminate option A.
- Check Option B: plates D, I, A: Arrange as A-D-I-D-A. Reading forward: A D I D A. Reading backward: A D I D A. This is a valid palindrome using all 5 plates exactly once.
- Verify options C and D are invalid: Neither C nor D can yield a 5-letter palindrome with all plates used exactly once.