Question
Seven students (P, Q, R, S, T, U and V) have different
heights. The height of the tallest person is 180cm. P is taller than T and immediately shorter than S. R is shorter than T but taller than V. S is not the tallest in the group. Q is shorter than only one person. What is the possible height of Q if the sum of U’s and S’s height is 345cm?Solution
Q is shorter than only one person. Height of the tallest person is 180cm. P is taller than T and immediately shorter than S. R is shorter than T but taller than V. S is not the tallest in the group. Inferences: From clue 1, we get Q is the 2nd tallest person. From clue 2, we get S > P > T From clue 3, we get T > R > V From clue 4, we get U > Q > S > P > T > R > V The final arrangement is as follows: U (Tallest - 180cm) > Q > S > P > T > R > V (Shortest) If the sum of U’s and S’s height is 345cm: U = 180cm S = 345 - 180 = 165cm Since Q is between U (180cm) and S (165cm), Q's possible height must be between 180 and 165. From the options, 170cm fits this criteria.
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