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

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

by AAPL » Tue Nov 21, 2017 8:27 am
If a certain positive integer is divided by 9, the remaider is 3. What is the remaider 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.

The OA is A.

Please, can any expert assist me with this DS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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Source: — Data Sufficiency |

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by ErikaPrepScholar » Wed Nov 22, 2017 9:49 am
We can approach this problem by building equations.

Let our integer = y. Then the question stem gives

y = 9a + 3

where a is some other integer.

Statement 1

y = 45b + 30

where b is some other integer. This simplifies to

y=5(9b + 6)

This means that y is divisible by 5, giving a remainder of 0. We can also think about it logically - 45 times any integer is divisible by 5, and 30 is divisible by 5, so 45b + 30 must be divisible by 5. Sufficient.

Statement 2

This tells us that y is even. Let's try some values given what we know from the question stem.

If a = 1, then y = 12, which gives a remainder of 2 when divided by 5. But if x =2, then y = 21, which gives a remainder of 1 when divided by 5, and if x = 3, then 7 = 30, which gives a remainder of 0 when divided by 5. Insufficient.
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