You have to decide whether the data given in the statements is sufficient to…

2025

You have to decide whether the data given in the statements is sufficient to answer the question or draw the conclusion asked in the question.

Mark 1 if statement A alone is sufficient but statement B alone is not sufficient.

Mark 2 if statement B alone is sufficient but statement A alone is not sufficient.

Mark 3 if both statements A and B together are needed.

Mark 4 if either statement A or statement B alone is sufficient.

Mark 5 if both statements together are not sufficient.

Is X greater than Y?

Statement A: X2+5X+6=0.

Statement B: Y2+16Y+63=0.

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

Show answer & explanation

Correct answer: C

Concept: In a Data Sufficiency comparison question, first solve the equation in each statement separately to find every value the variable can take under that statement. A statement is sufficient on its own only if it fixes the needed variable(s) enough to answer the question by itself. When each statement fixes only one of the two variables being compared, the comparison can be settled only by combining both statements and checking that every possible pairing of values gives the same result.

  1. Factor statement A: X2+5X+6=0 splits as X2+3X+2X+6=0, giving (X+3)(X+2)=0, so X=-3 or X=-2. Statement A alone fixes only X, with no information about Y, so it cannot settle whether X is greater than Y.

  2. Factor statement B: Y2+16Y+63=0 splits as Y2+9Y+7Y+63=0, giving (Y+9)(Y+7)=0, so Y=-9 or Y=-7. Statement B alone fixes only Y, with no information about X, so it also cannot settle the comparison on its own.

  3. Combine the two results: X can be -3 or -2, and Y can be -9 or -7.

  4. Check every pairing of an X value with a Y value: (-3,-9), (-3,-7), (-2,-9), (-2,-7).

  5. In every one of these four pairings, the X value is greater than the Y value.

Cross-check: the smallest possible X is -3 and the largest possible Y is -7; since -3 is still greater than -7, X > Y holds across the full range of values permitted by the two statements, not just in one pairing.

Because neither statement alone fixes both variables, but the two statements together always give X > Y, both statements A and B together are needed to answer the question.

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