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B, C, E, F and H have different heights. F is taller than E but shorter than B. E is taller than H. C is taller than H. More than two people are taller than C. How many people are taller than H?
One
Four
Three
Two
Four
Identify the minimum number of people taller than H by finding anyone taller than H directly or indirectly. Since F and C are taller than H, and F is taller than E (who is taller than H), while B is taller than F, and C has at least 3 people taller than C, H must be the shortest person among all 5 individuals.
Identify the minimum number of people taller than H by finding anyone taller than H directly or indirectly. Since F and C are taller than H, and F is taller than E (who is taller than H), while B is taller than F, and C has at least 3 people taller than C, H must be the shortest person among all 5 individuals.
Step 1: Write down direct height inequalities
From the given statements: 1) F is taller than E, but shorter than B, which gives B > F > E. 2) E is taller than H, giving E > H. Combining these gives B > F > E > H. 3) C is taller than H, giving C > H.
Step 2: Use the position constraint for C
We are given that 'More than two people are taller than C'. That means at least 3 people are taller than C. Since there are only 5 people total (B, C, E, F, H), if at least 3 people are taller than C, C can have at most 1 person shorter than C.
Step 3: Determine the relative order of all 5 people
We already know 4 people (B, F, E, C) are taller than H because: B > F > E > H, and C > H. Thus, H has 4 people taller than H (B, F, E, C), placing H at the bottom (5th position). The complete order from tallest to shortest is B > F > E > C > H.
A: Incorrect because only 1 person taller than H would mean H is 2nd tallest, which contradicts B > F > E > H. C: Incorrect because 3 people taller than H misses one of the people proven taller than H. D: Incorrect because 2 people taller than H contradicts B, F, E, and C all being taller than H.
B is correct because all 4 other individuals (B, C, E, and F) are taller than H, making H the shortest person with exactly 4 people taller than him.
Count how many distinct elements are explicitly or transitively stated to be greater than the target element; if all other elements are greater, the target element is the absolute minimum.
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