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P, Q, R, S, T and U are people such that R's height \(\lt\) S's height, T's height \(\gt\) Q's height, Q's height \(\gt\) P's height, T's height \(\lt\) R's height, and R's height = U's height. Who is the tallest among them?

  • A.R
  • B.S
  • C.Q
  • D.T

Answer: B

The tallest of the six is S.

From the conditions, T is shorter than R and R is shorter than S, so T < R < S. Also Q is shorter than T, and P is shorter than Q, and U has the same height as R. So the order is P < Q < T < R = U < S, which puts S at the top.

R is equal to U and below S, T is below R, and Q is shorter than T, so R, T and Q cannot be the tallest.

It helps to write the inequalities as a chain: P < Q < T < R = U < S. Everyone is placed between P at the bottom and S at the top, so S is clearly the tallest and P the shortest. The information that R and U are equal does not change this, because both are still below S.

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