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Recurring Decimal Integer Multiplier

CAT 2000 Slot 1 · Quantitative Ability · Easy · Number Systems

This is an easy Quantitative Ability question from the CAT 2000 Slot 1 paper. It tests Number Systems. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Let DD be a recurring decimal of the form D=0.a1a2a1a2a1a2…D = 0.a_1 a_2 a_1 a_2 a_1 a_2 \dots, where digits a1a_1 and a2a_2 lie between 00 and 99. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by DD?

  1. A.

    18

  2. B.

    108

  3. C.

    198

  4. D.

    288

Answer

C

Explanation

We can represent DD as D=10a1+a299D = \frac{10a_1 + a_2}{99}. Thus, multiplying DD by any multiple of 9999 will result in an integer. Among the choices, 198=99×2198 = 99 \times 2 is a multiple of 9999.

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