HCF Minimum Cartons Required

XAT 2010 · Quantitative Ability & Data Interpretation · Easy · Quantitative Ability

A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of same size. The number of boxes to be sent is 96 of brand A, 240 of brand B and 336 of brand C. These boxes are to be packed in cartons of same size containing equal number of boxes. Each carton should contain boxes of same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?

  1. A.

    20

  2. B.

    14

  3. C.

    42

  4. D.

    38

  5. E.

    16

Answer

B

Explanation

To minimize cartons, maximum boxes per carton =HCF(96,240,336)=48= \text{HCF}(96, 240, 336) = 48. Number of cartons =9648+24048+33648=2+5+7=14= \frac{96}{48} + \frac{240}{48} + \frac{336}{48} = 2 + 5 + 7 = 14.

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