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If a is an integer, is a-b an integer?

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If a is an integer, is a-b an integer? [#permalink]

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New post 02 May 2017, 00:42
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If a is an integer, is a-b an integer?

1) 100 is a factor of a
2) b is 37 percent of a
[Reveal] Spoiler: OA

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If a is an integer, is a-b an integer? [#permalink]

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New post 02 May 2017, 06:36
If a is an integer, is a-b an integer?

S1) 100 is a factor of a

No mention of b. Insufficient!

S2) b is 37 percent of a

If a = 100, then b = 37. a-b is an integer.
If a = 1, then b=0.37. a-b is not an integer.

Insufficient!

S1+S2

If a is multiple of 100, so a can be 100, 200, 300, 400 etc.

37% of any multiple of 100 will be an integer.

Integer -Integer = Integer.

Sufficient!

Hence, C is the answer.

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Math Revolution GMAT Instructor
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Re: If a is an integer, is a-b an integer? [#permalink]

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New post 04 May 2017, 00:18
==> If you modify the original condition and the question and check the question again, from a-b=int?, int-b=int?, you get b=int-int=int?. Since there is 2 variables (a,b), in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), you get b=0.37a=0.37(100int)=37int=int, hence it is always yes and sufficient.

Therefore, the answer is C.
Answer: C
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Re: If a is an integer, is a-b an integer?   [#permalink] 04 May 2017, 00:18
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