Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T,…
2025
Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies P<Q, S>P>T, R<T. If integers 1 through 5 are used to construct such a number, the value of P is:
Answer: C. 3 — The five distinct digits must be a permutation of 1, 2, 3, 4, and 5. The inequalities $R<T<P$ and $P<Q$, $S>P$ require two distinct digits below \(P\) (namely…
- A.
1
- B.
2
- C.
3
- D.
4
Show answer & explanation
Correct answer: C
The five distinct digits must be a permutation of 1, 2, 3, 4, and 5. The inequalities $R<T<P$ and $P<Q$, $S>P$ require two distinct digits below \(P\) (namely $R,T$) and two distinct digits above \(P\) (namely $Q,S$). Among 1 through 5, only $P=3$ has exactly two smaller digits and two larger digits. Therefore the value of \(P\) is 3.
Loading lesson…