Ok. Finally a simple question.

What is the value of the positive integer \(n\)?Statement A: If \(31\), \(32\), and \(33\) are each divided by \(n\), the reminders are \(7\), \(0\), and \(1\), respectively.

Let's check \(31\) . Since remainder is \(7\), the number has to be bigger than \(7\).

Hence for \(31\) the positive integer could be \(8\), \(12\), or \(24\). So three possibilities so far.

Let's check \(32\) . Since remainder is \(0\), the number can be any fraction of \(32\) .

Let's check \(33\) . Since remainder is \(1\), the number can be 2, 4, 8, or any factor of \(32\) for that matter .

The only overlap is the number \(8\) so \(n\) must be \(8\) or to see it in a different light (and that is why i mentioned factors of 32 in the first instance), the only factor of \(32\) that fits the bill for \(31\) is \(8\). Hence

Sufficient.

Statement 2: n is an even number. Can be any even number. Hence

Insufficient.

Answer:

A
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