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Ratio Product Evaluation

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 ab=13\frac{a}{b} = \frac{1}{3}, bc=2\frac{b}{c} = 2, cd=12\frac{c}{d} = \frac{1}{2}, de=3\frac{d}{e} = 3 and ef=14\frac{e}{f} = \frac{1}{4}, then what is the value of abcdef\frac{abc}{def}?

  1. A.

    3/8

  2. B.

    27/8

  3. C.

    3/4

  4. D.

    27/4

  5. E.

    1/4

Answer

3/8

Explanation

We want abcdef=(af)(be)(cd)\frac{abc}{def} = \left(\frac{a}{f}\right) \left(\frac{b}{e}\right) \left(\frac{c}{d}\right). Note that: af=ab⋅bc⋅cd⋅de⋅ef=13⋅2⋅12⋅3⋅14=14\frac{a}{f} = \frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{d} \cdot \frac{d}{e} \cdot \frac{e}{f} = \frac{1}{3} \cdot 2 \cdot \frac{1}{2} \cdot 3 \cdot \frac{1}{4} = \frac{1}{4}. be=bc⋅cd⋅de=2⋅12⋅3=3\frac{b}{e} = \frac{b}{c} \cdot \frac{c}{d} \cdot \frac{d}{e} = 2 \cdot \frac{1}{2} \cdot 3 = 3. cd=12\frac{c}{d} = \frac{1}{2}. So abcdef=14×3×12=38\frac{abc}{def} = \frac{1}{4} \times 3 \times \frac{1}{2} = \frac{3}{8}.

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