Seven boxes P, Q, R, S, T, U and V are kept one above another such that the…
2024
Seven boxes P, Q, R, S, T, U and V are kept one above another such that the bottommost box is numbered as box 1 while the topmost box is numbered as box 7. There are two boxes between R and S(R is above S). Box Q is the topmost box. Box T is adjacent to box S. Box V is an even-numbered box just above box T. Box U is below box P.How many boxes are above box R?
- A.
Three
- B.
Two
- C.
One
- D.
Four
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Show answer & explanation
Correct answer: B
Final answer: Two boxes are above R.
Key constraints:
Box Q is at the top (position 7).
R is three places above S (there are two boxes between them).
T is adjacent to S; V is immediately above T and V must be on an even-numbered position.
U is below P (P is above U).
Reasoning (check possible positions for R and S):
If R is at position 6, then S would be at position 3. T would be at 2 or 4, making V at 3 or 5, both odd positions — this contradicts V being even. So this case fails.
If R is at position 4, then S would be at position 1. T must be at 2 (adjacent to S), making V at 3 (odd) — again V would be odd, so this case fails.
If R is at position 5, then S is at position 2. T can be at position 3 with V at position 4 (even) — this satisfies the parity and adjacency constraints. The remaining two boxes must be placed so that P is above U, which fits with placing P at 6 and U at 1.
Final valid arrangement (top to bottom, positions 7 to 1):
7: Q
6: P
5: R
4: V
3: T
2: S
1: U
Therefore, there are two boxes above R (P and Q).