QUESTION

CSAT

Easy

Maths

Prelims 2022

A person X wants to distribute some pens among six children A B C D E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

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Explanation

The number of pens each child gets must be an even number.

Start with the LCM approach: If there were no restrictions on the number of pens being even, we would start by calculating the LCM of 2, 3, 4, 5, and 6, which is 60. Therefore, we initially set $x = 60$ .

Using this: A gets $2x = 2 \times 60 = 120$ pens. B gets $x = 60$ pens. C gets $x/2 = 60/2 = 30$ pens. D gets $x/4 = 60/4 = 15$ pens. E gets $x/5 = 60/5 = 12$ pens. F gets $x/6 = 60/6 = 10$ pens.

Address the Even Number Condition: As we can see from the values above: A gets 120 pens (even), B gets 60 pens (even), C gets 30 pens (even), D gets 15 pens (odd), E gets 12 pens (even), F gets 10 pens (even).

Since D's count (15 pens) is odd, we cannot proceed with 60 pens. To make all the numbers even, we multiply all the values by 2.