Discussion
Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions:
\(P \lt Q\)
\(S \gt P \gt T\)
\(R \lt T\)
If integers 1 through 5 are used to construct such a number, the value of P is:
Answer: C
P is 3.
Combine the conditions: R < T, T < P, P < S and P < Q. So R and T are smaller than P, and S and Q are larger.
With the digits 1 to 5, exactly two are below P and two above, so P must be the middle value, 3. Then R = 1, T = 2, and S and Q are 4 and 5 in some order (for example 34152).
P = 1 or 2 would leave too few digits below it for R and T, and P = 4 too few above it for S and Q.
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