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Grain Sales Sequence

CAT 2024 Slot 1 · Quantitative Ability · Easy · Word Problems

This is an easy Quantitative Ability question from the CAT 2024 Slot 1 paper. It tests Word Problems. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

  1. A.

    18

  2. B.

    36

  3. C.

    50

  4. D.

    42

Answer

D

Explanation

Working backwards:

  • Before 3rd customer: x32−3=0  ⟹  x3=6\frac{x_3}{2} - 3 = 0 \implies x_3 = 6 kg.
  • Before 2nd customer: x22−3=6  ⟹  x22=9  ⟹  x2=18\frac{x_2}{2} - 3 = 6 \implies \frac{x_2}{2} = 9 \implies x_2 = 18 kg.
  • Before 1st customer: x12−3=18  ⟹  x12=21  ⟹  x1=42\frac{x_1}{2} - 3 = 18 \implies \frac{x_1}{2} = 21 \implies x_1 = 42 kg.

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