Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

When solving such logic puzzles with digit constraints, list available digits and test possible combinations systematically to satisfy all inequalities.

Answer 1

The Correct Option is C

We are given the constraints: \[ P<Q,\quad S>P>T,\quad R<T \] We need to assign the digits 1 through 5 (each used only once) to P, Q, R, S, and T in a way that satisfies all the above conditions. Let’s try to assign values that satisfy these relations step-by-step: From \( S>P>T \), we can choose: \[ S = 5,\quad P = 3,\quad T = 2 \] This satisfies \( S>P>T \). Now for \( P<Q \), if \( P = 3 \), then \( Q \) must be greater than 3, so we can take: \[ Q = 4 \] That leaves only 1 unused, which can go to: \[ R = 1 \] Now check if all conditions are satisfied: - \( P = 3<Q = 4 \) ✔️ - \( S = 5>P = 3>T = 2 \) ✔️ - \( R = 1<T = 2 \) ✔️ All conditions are satisfied. Thus, the value of \( P \) is 3.