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If a certain positive integer is divided by 9, the .....

by M7MBA » Fri Apr 05, 2019 11:16 am

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If a certain positive integer is divided by 9, the remainder is 3. What is the remainder when the integer is divided by 5?

(1) If the integer is divided by 45, the remainder is 30.
(2) The integer is divisible by 2.

[spoiler]OA=A[/spoiler]

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by Ian Stewart » Fri Apr 05, 2019 4:00 pm

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Statement 1 tells us our number is 30 greater than some multiple of 45, so our number is equal to 45q + 30, for some integer q. But 45q + 30 = 5(9q + 6), which is clearly divisible by 5, so the remainder is 0 when we divide our number by 5, and Statement 1 is sufficient, even without using any information from the question stem.

Statement 2 is not sufficient, because knowing about division by 2 and by 9 tells you nothing about division by 5 -- there's just no relationship between those things. Here our number could be 12, or it could be 30, among other possibilities, and we can get different answers to the question (in fact you can get any answer at all, between 0 and 4 inclusive).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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