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Prime Number of Employees Ratio

CAT 2006 Slot 1 · Quantitative Ability · Easy · Quantitative Aptitude

This is an easy Quantitative Ability question from the CAT 2006 Slot 1 paper. It tests Quantitative Aptitude. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

  1. A.

    101 : 88

  2. B.

    87 : 100

  3. C.

    110 : 111

  4. D.

    85 : 98

  5. E.

    97 : 84

Answer

97 : 84

Explanation

Total employees must be a multiple of the sum of terms in the ratio. Check the sum of terms for each option:

  1. 101+88=189101 + 88 = 189 (Composite)
  2. 87+100=187=11×1787 + 100 = 187 = 11 \times 17 (Composite)
  3. 110+111=221=13×17110 + 111 = 221 = 13 \times 17 (Composite)
  4. 85+98=183=3×6185 + 98 = 183 = 3 \times 61 (Composite)
  5. 97+84=18197 + 84 = 181 (Prime number < 300)

Only option 5 yields a prime sum.

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