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

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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.

The OA is A

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by Ian Stewart » Thu Aug 29, 2019 6:31 am

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Statement 1 tells us the number is 30 greater than a multiple of 45, so it is 30 greater than a multiple of 5, and must be itself a multiple of 5. So the remainder will be zero when we divide the number by 5, and Statement 1 is sufficient.

Using Statement 2, we know we get a remainder of 3 when we divide by 9, and a remainder of 0 when we divide by 2. Division by 2 and 9 have nothing to do with division by 5, so this information won't be useful -- we can get any remainder at all when we divide the number by 5. For example, the number could be 12, and the remainder could be 2 when we divide by 5, or the number could be 30, and the remainder could be 0 when we divide by 5 (and if you test larger numbers, you can get any other remainder - 48, 66, and 84 give the remainders 3, 1 and 4, respectively when you divide by 5).

So the answer is A.
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