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Value of Reciprocal Difference in Exponents

CAT 2019 Slot 1 · Quantitative Ability · Hard · Exponents

This is a hard Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Exponents. 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 (5.55)x=(0.555)y=1000(5.55)^x = (0.555)^y = 1000, then the value of 1x−1y\frac{1}{x} - \frac{1}{y} is

  1. A.

    1

  2. B.

    \frac{1}{3}

  3. C.

    \frac{2}{3}

  4. D.

    3

Answer

B

Explanation

(5.55)x=103  ⟹  5.55=103/x(5.55)^x = 10^3 \implies 5.55 = 10^{3/x}. Also, (0.555)y=103  ⟹  0.555=103/y(0.555)^y = 10^3 \implies 0.555 = 10^{3/y}. Dividing the two expressions: 5.550.555=103/x103/y  ⟹  10=103(1/x−1/y)\frac{5.55}{0.555} = \frac{10^{3/x}}{10^{3/y}} \implies 10 = 10^{3(1/x - 1/y)}. Thus, 3(1x−1y)=1  ⟹  1x−1y=133\left(\frac{1}{x} - \frac{1}{y}\right) = 1 \implies \frac{1}{x} - \frac{1}{y} = \frac{1}{3}.

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