Study the following information carefully and answer the questions given below:
Six persons — A, B, C, D, E and F — have different heights, but not necessarily in the same order. More than two persons are shorter than E. C is two persons taller than E. Height of tallest person is 182cm. Height of A is 156cm. F is shorter than A. Only two persons are shorter than D. B is taller than A but shorter than C.
Who among the following is third shortest?
Correct Answer :
D
Solution :
To find who is the third shortest person, let us analyze the clues step-by-step to determine the heights of all six individuals from tallest (1st) to shortest (6th):
Let the six positions be represented as follows:
1 (Tallest) > 2 > 3 > 4 > 5 > 6 (Shortest)
Step 1: Position D based on the clues.
We are told: "Only two persons are shorter than D."
This means there are exactly two positions below D (positions 5 and 6). Thus, D must be in the 4th position:
_ > _ > _ > D > _ > _
Step 2: Position E and C based on the clues.
We are told: "More than two persons are shorter than E." This means at least 3 persons are shorter than E. Thus, E must be in position 1, 2, or 3.
We are also told: "C is two persons taller than E." This means C must be placed two positions above E (i.e., C > [one person] > E).
If E were in position 2, C would have to be in a position above 1, which is impossible. Similarly, if E were in position 1, C cannot be taller than E.
Therefore, E must be in position 3, and C must be in position 1:
C > _ > E > D > _ > _
Step 3: Position the remaining persons (A, B, and F).
The vacant positions are 2, 5, and 6.
We are given:
- "B is taller than A but shorter than C."
- "F is shorter than A."
Combining these relations gives us the order: C > B > A > F.
Since C is already in position 1, B must occupy position 2, A must occupy position 5, and F must occupy position 6.
The final order from tallest to shortest is:
C (182 cm) > B > E > D > A (156 cm) > F
Step 4: Identify the third shortest person.
Looking at the order from shortest to tallest:
1. Shortest: F
2. Second shortest: A
3. Third shortest: D
Therefore, the third shortest person is D.
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