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Smallest Value for Negative Fraction

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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If x=−0.5x = -0.5, then which of the following has the smallest value?

  1. A.

    1 / (2^x)

  2. B.

    1 / x

  3. C.

    1 / (x^2)

  4. D.

    2^x

  5. E.

    1 / sqrt(-x)

Answer

1 / x

Explanation

For x=−0.5x = -0.5:

  1. 12x=20.5=2≈1.414\frac{1}{2^x} = 2^{0.5} = \sqrt{2} \approx 1.414
  2. 1x=1−0.5=−2\frac{1}{x} = \frac{1}{-0.5} = -2
  3. 1x2=10.25=4\frac{1}{x^2} = \frac{1}{0.25} = 4
  4. 2x=2−0.5=12≈0.7072^x = 2^{-0.5} = \frac{1}{\sqrt{2}} \approx 0.707
  5. 1−x=10.5=2≈1.414\frac{1}{\sqrt{-x}} = \frac{1}{\sqrt{0.5}} = \sqrt{2} \approx 1.414

The only negative value is 1x=−2\frac{1}{x} = -2, which is the smallest.

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