Directions: Each of the questions below consists of a question and two…
2020
Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and answer the following question.
Eight boxes P, Q, R, S, T, U, V and W are arranged one above the other but not necessarily in the same order. Which of the following boxes is placed just below the box U?
Statement I: More than three boxes are placed between S and T, where T is placed below box S. Box Q and S are placed adjacent to each other. Two boxes are placed between U and Q. Only one box is placed between P and T.
Statement II: One box is placed between Q and R. Two boxes are placed between P and Q. One box is placed between T and R. Box P is not adjacent to box T. Box U is placed exactly in between box P and the box which is placed just above box R.
- A.
If the data in statement I alone are sufficient to answer the question.
- B.
If the data in statement II alone are sufficient to answer the question.
- C.
If the data either in statement I alone or in statement II alone are sufficient to answer the question.
- D.
If the data given in both I and II together are not sufficient to answer the question.
- E.
If the data in both the statements I and II together are necessary to answer the question.
Show answer & explanation
Correct answer: B
Concept
In a data-sufficiency problem you do NOT find the final value — you only judge whether each statement, used alone, pins down the queried position uniquely. A statement is sufficient only if every arrangement that satisfies it gives the SAME answer to the asked question; if even two valid arrangements disagree, that statement is insufficient. Test each statement independently before combining.
Use eight floors numbered 1 (top) to 8 (bottom); "below" means a larger number and "just below X" means the floor directly under X. "More than three boxes between" two boxes means a gap of at least five positions; "exactly in between" means the box sits at the midpoint, equidistant from the two reference boxes.
Applying Statement I alone
Encode the clues: T is below S with more than three boxes between them (so S and T are far apart, S above T); Q is adjacent to S; two boxes lie between U and Q (a gap of three); one box lies between P and T (a gap of two).
Working through every arrangement that fits these clues, the box that ends up just under U is not forced to a single identity — different valid layouts place different boxes there:
The box just under U can come out as P in one valid layout,
as V or W in others,
and as R or T in still others.
Because more than one outcome is possible, Statement I alone cannot fix a unique box below U — it is INSUFFICIENT.
Applying Statement II alone
Encode the clues: one box between Q and R (gap of two); two boxes between P and Q (gap of three); one box between T and R (gap of two); P is not adjacent to T; and U lies exactly in between P and the box directly above R.
These conditions lock a rigid skeleton. P is forced to the top; the chain P … U … Q and the R–T spacing then force the following fixed slots, with only S, V, W free to swap among the leftover floors:
Floor (top→bottom) | Fixed box |
|---|---|
1 | P |
3 | U |
4 | Q |
6 | R |
8 | T |
U is fixed on floor 3 and Q on floor 4 in EVERY arrangement that satisfies Statement II. The free boxes S, V, W only fill floors 2, 5 and 7, so they never land between U and Q.
So the box just below U is uniquely Q. Statement II alone determines the answer — it is SUFFICIENT.
Cross-check / conclusion
Statement I alone → multiple possible boxes below U → insufficient.
Statement II alone → forces Q below U → sufficient.
Since one statement alone settles the question while the other does not, the choice asserting that the second statement by itself is enough is the correct one. The required box below U is Q.