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Data Sufficiency - Prime Number Properties

CAT 1991 Slot 1 · Quantitative Ability · Easy · Data Sufficiency

This is an easy Quantitative Ability question from the CAT 1991 Slot 1 paper. It tests Data Sufficiency. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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What is the value of prime number xx?

I. x2+xx^2 + x is a two digit number greater than 50. II. x3x^3 is a three digit number.

  1. A.

    If the question can be answered with the help of statement I alone

  2. B.

    If the question can be answered with the help of statement II alone

  3. C.

    If both statement I and statement II are needed to answer the question

  4. D.

    If the question cannot be answered even with the help of both statements

Answer

A

Explanation

From Statement I: 50<x(x+1)<10050 < x(x+1) < 100. Testing prime numbers:

  • For x=7x = 7, 7×8=567 \times 8 = 56, which satisfies 50<56<10050 < 56 < 100.
  • For x=11x = 11, 11×12=132>10011 \times 12 = 132 > 100.
  • For x=5x = 5, 5×6=30<505 \times 6 = 30 < 50. Only x=7x = 7 satisfies Statement I alone.

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