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If x and y are positive integers such that x = 8y + 12, what is the

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If x and y are positive integers such that x = 8y + 12, what is the [#permalink]

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New post 21 Aug 2017, 08:00
Hello All,

My take on this question:

As given , x = 8y+12 and x and y are positive integers.

Statement 1: x = 12u, u is integer

It means x is multiple of 12. But x is also 8y+12 then it means 8y should also be multiple of x, which in turn means y can take values 3 , 6, 9 ...etc i.e. multiple of 3.
Case 1: say y = 3 then x = 8*3 + 12 = 36 , GCD(x,y) = 3
Case 2: say y = 6 then x = 8*6 +12 = 60, GCD(x,y) = 6

Clearly 1 insufficient.

Statement 2: y = 12u, u is integer

It means y is multiple of 12 , which in turn means x = 8(multiple of 12) + 12 i.e. x is nothing but the next multiple of 12 than y or y and x are consecutive multiples of 12.
So GCD of two consecutive multiples of 12 should be 12 ,hence sufficient. Answer B.

Hope it helps.

Thanks
Manoj Parashar
If x and y are positive integers such that x = 8y + 12, what is the   [#permalink] 21 Aug 2017, 08:00

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