Question

Eight boxes - A, B, C, D, P, Q, R and S are stacked vertically but not necessarily in the same order. Which among them is kept immediately above R?
Statement (I): Only three boxes are kept above D and only one box is kept between D and Q. Q is kept lower than D and is immediately below P.
Statement (II): Only one box is kept between A and C. C is kept three boxes above Q. As many boxes are kept above B as are kept below R.

• A. Only statement I is sufficient to answer the question.
• B. Only statement II is sufficient to answer the question.
• C. Statement I and statement II together are sufficient to answer the question.
• D. Statement I and statement II together are not sufficient to answer the question.

Hint:

In stacking puzzles, it's helpful to draw 8 slots and fill them in as you deduce information. Be careful with phrasing like "X boxes above" vs "X boxes between". "C is three boxes above Q" usually means C's position number is 3 greater than Q's.

Answer 1

The Correct Option is C

Step 1: Analyze Statement (I) alone.

- There are 8 positions (1=bottom, 8=top).
- "Only three boxes are kept above D" \(\rightarrow\) D is at position 5. (Boxes at 6,7,8 are above).
- "one box is kept between D and Q" and "Q is kept lower than D" \(\rightarrow\) D is at 5, so Q is at position 3.
- "Q is immediately below P" \(\rightarrow\) P is at position 4.
- From (I), we have the partial stack: __ __ __ P(4) Q(3) __ __. D is at 5. So: __ __ __ D(5) P(4) Q(3) __ __.
- Statement I is insufficient because we don't know the position of R or the box above it.

Step 2: Analyze Statement (II) alone.

- "Only one box is kept between A and C" \(\rightarrow\) A __ C or C __ A.
- "C is three boxes above Q" \(\rightarrow\) C is at position x, Q is at x-4. (e.g. C=5, Q=1 or C=8, Q=4).
- "As many boxes are kept above B as are kept below R" \(\rightarrow\) If B is at position n, R is at 9-n. (e.g. B=8, R=1; B=7, R=2 etc.). They are symmetrical.
- Statement II is insufficient because it provides relative positions, not absolute positions. We cannot locate R.

Step 3: Analyze both statements together.

- From (I): D=5, P=4, Q=3.
- Now use (II) with this information: "C is three boxes above Q". Since Q=3, C must be at position 3+4=7.
- Now use "Only one box is kept between A and C". Since C=7, A must be at position 5. But D is at position 5. This creates a contradiction.

Re-examining "C is three boxes above Q". This implies three boxes between them: C __ __ __ Q. If Q=3, C=7. This is correct.
"Only one box is kept between A and C". C=7, so A must be at 5 or 9. 9 is not possible. So A=5. This means A and D are in the same spot (position 5). The statements are contradictory.

Re-interpreting "C is kept three boxes above Q" to mean C is at Q's position + 3 = 3+3=6.
If C=6, then "one box between A and C" means A=4 or A=8. A=4 is not possible as P is there. So A=8.
- So far: A=8, C=6, D=5, P=4, Q=3.
- Positions left: 1, 2, 7. Boxes left: B, R, S.
- Now use "As many boxes above B as below R". Let's test the remaining spots.
- If B=7 (1 above), then R=2 (1 below). This works. S would be at position 1.
- This gives a complete valid arrangement: A(8), B(7), C(6), D(5), P(4), Q(3), R(2), S(1).
- The question is "Which box is kept immediately above R?". In this arrangement, R is at position 2. The box at position 3 is Q.
- Since we have a unique arrangement and can answer the question, both statements together are sufficient.