Directions : Each of the questions below consists of a question and two…

2022

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 questions.

Nine persons of different heights are arranged in descending order according to their height. Who among the following is the 3rd tallest?
Statement I: Two persons are between Q and R. P is shorter than S but not just shorter. The number of persons between R and S is same as the number of persons between Q and R. T and U are not shorter to S. More than two persons between P and U. T is taller than R.
Statement II: Only two persons are shorter to Q. One person is between Q and V. No one is between V and R. The number of persons between R and Q is same as the number of persons taller to T. U is taller than T and shorter than S.

  1. A.

    If the data in statement I alone are sufficient

  2. B.

    If the data in statement II alone are sufficient

  3. C.

    If the data either in statement I alone or statement II alone are sufficient to answer

  4. D.

    If the data given in both I and II together are not sufficient

  5. E.

    If the data given in both the statements I and II together are necessary to answer

Show answer & explanation

Correct answer: B

Concept

In a data-sufficiency problem you do NOT solve for the final value first. For each statement you ask one thing only: does the information in that statement, by itself, force a single answer to the asked question (here, a single name in the queried slot)? If the answer to the question can still vary, that statement is not sufficient. Treat the two statements independently before considering them together.

Frame

Nine persons stand in descending order of height. Number the slots 1 to 9, where slot 1 is the tallest and slot 9 the shortest. The question asks only who occupies slot 3 (the 3rd tallest). Sufficiency means: the clues fix the occupant of slot 3 with no other possibility, even if some unrelated slots stay free.

Testing Statement I

Apply the clues of the first statement only:

  1. Two persons stand between Q and R, so the height gap between their slots is 3.

  2. The persons between R and S equal those between Q and R, so the R-to-S gap is also 3.

  3. P is shorter than S but not immediately below S, T and U are both taller than S, more than two persons separate P and U, and T is taller than R.

Working these constraints through, more than one seating still survives and slot 3 can be filled by different persons across those seatings (the 3rd-tallest is not pinned to a single name). Because the queried slot is not forced to one person, the first statement on its own cannot name the 3rd tallest.

Testing Statement II

Now use the second statement only:

  1. Only two persons are shorter than Q, so Q is fixed at slot 7 (slots 8 and 9 lie below).

  2. One person stands between Q and V, placing V at slot 5 (slot 6 is the single person between them).

  3. No one stands between V and R, so R is adjacent to V at slot 4.

  4. The persons between R (slot 4) and Q (slot 7) number two; this must equal the persons taller than T, so two persons are taller than T, fixing T at slot 3.

  5. U is taller than T and shorter than S, which seats U at slot 2 and S at slot 1.

This forces the named persons into a single order at the top: S, U, T, R, V at slots 1 to 5 and Q at slot 7. The three remaining persons fall into slots 6, 8 and 9 and may sit there in any order, but that does not affect the question. Slot 3 is forced to be T with no alternative, so the second statement alone settles the asked question.

Cross-check

Verify against every clue of Statement II: two people are shorter than Q (slots 8, 9); exactly one person sits between Q and V; R is next to V with nobody between; the count between R and Q (two) matches the count taller than T (two); and S > U > T holds. All clues are satisfied, and slot 3 is uniquely T.

Conclusion

Statement I leaves the 3rd-tallest slot open to several persons, while Statement II forces T into slot 3 regardless of how the unrelated slots fill. So Statement II alone is sufficient and Statement I alone is not.

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