During a sale, colour pencils were being sold in packs of 24 each and crayons in packs of 32 each. If you want full packs of both and the same number of pencils and crayons, how many of each would you need to buy?

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4 and 3

2 and 5

6 and 10

1 and 3

answer is D.

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Detailed Solution

Given that the number of colour pencils in a pack is 24 and the number of crayons in each pack is 32.
Factorise the numbers 24 and 32:

24 = 2^{3} \times 3

\Rightarrow 32 = 2^{5}

\Rightarrow LCM (24, 32) = 96

In 1 pack there are 24 pencils.

\Rightarrow 96 = 4 \times 24

\Rightarrow

4 packs of pencils need to be brought.
In 1 pack there are 32 crayons.

\Rightarrow 96 - 3 \times 32

\Rightarrow

3 packs of crayons need to be brought.
Therefore, 4 packs of pencils and 3 packs of crayons should be brought.
Hence, option 4 is correct.

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