GATE 2026 DA – Question 9
$P, Q, R, S, X$, and $Y$ are distinct single-digit whole numbers taking values from 0 to 9.
$PQ$ is a two-digit number with $Q$ being in the units place and $P$ in the tens place. Similarly, $RS$ is a two-digit number.
It is known that $PQ$ and $RS$ are consecutive numbers and $(PQ)^2 + (RS)^2 = XYP$, with $XYP$ being a three-digit number.
The value of $Y$ is __________
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Correct answer: (C) 6
Explanation
The squares of two consecutive two-digit numbers add up to a three-digit number whose last digit is the tens digit $P$ of the first number. Trying the consecutive pairs, $19^2 + 20^2 = 361 + 400 = 761$ gives $P = 1$, $Q = 9$, $R = 2$, $S = 0$, $X = 7$, $Y = 6$, and the six digits 1, 9, 2, 0, 7, 6 are all different. It is the only pair that works, so $Y = 6$.