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If the positive integer \(x\) is rounded to the nearest ten,

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by AAPL » Sat May 04, 2019 3:18 am

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Manhattan Prep

If the positive integer \(x\) is rounded to the nearest ten, will the result be greater than \(x\)?

1) If \(x\) is divided by 10, the remainder is even.
2) If \(x\) is divided by 5, the remainder is odd.

OA C
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Source: — Data Sufficiency |

by Ian Stewart » Sat May 04, 2019 5:25 am
The question is just asking "is the units digit of x greater than 5?"

When we divide a positive number by 10, the remainder we get is that number's units digit, so Statement 1 tells us "the units digit of x is even". It could be 0, 2, 4, 6 or 8, so we can't answer the question.

When we divide a positive number by 5, the remainder we get will be that number's units digit, if the units digit is between 0 and 4 inclusive. If the number's units digit is between 5 and 9 inclusive, we'll need to subtract 5 from the units digit to find the remainder (so, for example, when we divide 329 by 5, the remainder is 9-5 = 4). So Statement 2 tells us that the units digit of x is 1, 3, 6 or 8, and we can't answer the question.

Using both Statements, looking at where our possibilities overlap, the units digit of x can only be 6 or 8, and in either case, when we round x to the nearest ten, we'll round up, so the answer is C.
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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