Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions: P P > T R < T If integers 1 through 5 are used to construct such a number, the value of P is:

GATE 2025 MN – Question 8

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 2 marks · Multiple choice

Consider a five-digit number $PQRST$ that has distinct digits $P$, $Q$, $R$, $S$, and $T$, and satisfies the following conditions:

$P < Q$
$S > P > T$
$R < T$

If integers 1 through 5 are used to construct such a number, the value of $P$ is:

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Show answer and explanation

Correct answer: (C) 3

Explanation

From $R < T < P < S$ and $P < Q$, the digit $P$ is bigger than $R$ and $T$ and smaller than $S$ and $Q$. With the digits 1 to 5 the smallest two must be $R = 1$ and $T = 2$, the next is $P = 3$, and $S$ and $Q$ are 4 and 5. So $P = 3$.

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