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

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by Ian Stewart » Sat May 04, 2019 5:25 am

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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.
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