Question by Summer Clouds - Discuss with MathYouLike

Summer Clouds moderators

24/08/2017 at 08:52

Parisa sets her marbles in groups of equal size on the desk. After she arranged the marbles in groups of 3, she found that there were 2 marbles left. Then she arranged the marbles in groups of 5, and again there were 2 marbles left. At least how many more marbles does she need so that there won't be any left when she arranges them in groups of 3 and in groups of 5?

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VTK-VangTrangKhuyet 24/08/2017 at 14:20

Call the number of marbles is a.

Following thread we have : \(\left(a-2\right)⋮3\) and \(\left(a-2\right)⋮5\)

So we take an example that \(32:3=10\left(remainder-2\right)\)and \(32:5=6\left(remainder-2\right)\)

So at least she needs 13 more marbles so that 32 + 13 = 55 marbles which is divisible for 3 and 5 => there won't be any left when she arranges them in groups of 3 and in groups of 5.

So the answer is 13.

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