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    Question

    A, B, C, D, E, and F, each have different heights. Only

    one person is taller than C. The shortest height is 160 cm. A is 170 cm tall. The tallest height is 174 cm. F is shorter than A but taller than D. B is not 160 cm tall. D is 162 cm tall. What can be the possible height of F?
    A 161 cm Correct Answer Incorrect Answer
    B 172 cm Correct Answer Incorrect Answer
    C 171 cm Correct Answer Incorrect Answer
    D 166 cm Correct Answer Incorrect Answer

    Solution

    F can be 164 cm, 166 cm, or 168 cm .

    Reasoning (concise):

    • Six people have distinct heights; shortest = 160 , tallest = 174 .

    • D = 162 , A = 170 .

    • “Only one person is taller than C” ⇒ C is second tallest , so the tallest (174) is someone else.

    • B is not 160 , and F is shorter than A (170) but taller than D (162) ⇒ F must be one of 164, 166, 168.

    • 160 cannot be B (B ≠ 160) and cannot be A, D, or F (given values/constraints), so 160 must be E; 174 must be B; C becomes the remaining highest value (e.g., 172).

    • All three candidates 164, 166, 168 for F are consistent with the conditions.

    Hence F = 164 cm or 166 cm or 168 cm .

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