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Data Sufficiency Questions

XAT 2010 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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Passage / data set

Questions are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

  • A. Statement I alone is sufficient to answer the question.
  • B. Statement II alone is sufficient to answer the question.
  • C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
  • D. Either Statement I or Statement II alone is sufficient to answer the question.
  • E. Both Statement I and Statement II are insufficient to answer the question

Question 1 of 2

In the trapezoid PQRS, PS is parallel to QR. PQ and SR are extended to meet at A. What is the value of ∠PAS\angle PAS ? I. PQ=3PQ = 3, RS=4RS = 4 and ∠QPS=60∘\angle QPS = 60^\circ. II. PS=10PS = 10, QR=5QR = 5.

  1. A.

    Statement I alone is sufficient to answer the question.

  2. B.

    Statement II alone is sufficient to answer the question.

  3. C.

    Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

  4. D.

    Either Statement I or Statement II alone is sufficient to answer the question.

  5. E.

    Both Statement I and Statement II are insufficient to answer the question

Answer

A

Explanation

From Statement I: In △AQR∼△APS\triangle AQR \sim \triangle APS, with side lengths PQ=3,RS=4PQ=3, RS=4 and angle ∠QPS=60∘\angle QPS=60^\circ, trigonometric relationships allow uniquely determining all angles of △APS\triangle APS, including ∠PAS\angle PAS. Statement I alone is sufficient.

Question 2 of 2

A sequence of positive integer is defined as An+1=An2+1A_{n+1} = A_n^2 + 1 for each n≥0n \ge 0. What is the value of Greatest Common Divisor of A900A_{900} and A1000A_{1000} ? I. A0=1A_0 = 1 II. A1=2A_1 = 2

  1. A.

    Statement I alone is sufficient to answer the question.

  2. B.

    Statement II alone is sufficient to answer the question.

  3. C.

    Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

  4. D.

    Either Statement I or Statement II alone is sufficient to answer the question.

  5. E.

    Both Statement I and Statement II are insufficient to answer the question

Answer

D

Explanation

Statement I gives A0=1  ⟹  A1=2A_0 = 1 \implies A_1 = 2. Statement II gives A1=2A_1 = 2. Either statement uniquely fixes the entire sequence and its GCDs. Hence either statement alone is sufficient.

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