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11 Nov 2021, 03:16
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Is positive integer x odd?
(1) The product of any two distinct positive factors of x is odd.
(2) The difference of any two distinct positive factors of x is even.
(1) The product of any two distinct positive factors of x is odd.
(2) The difference of any two distinct positive factors of x is even.
11 Nov 2021, 03:16
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Official Solution:
Is positive integer \(x\) odd?
(1) The product of any two distinct positive factors of \(x\) is odd.
\(x\) cannot be even because if it is then it has 1 and 2 as factors and \(1*2=2=even\). Thus \(x\) must be odd. In this case all its factors will be odd and the product of any two distinct positive factors of \(x\) will be odd. Sufficient.
(2) The difference of any two distinct positive factors of \(x\) is even.
\(x\) cannot be even because if it is then it has 1 and 2 as factors and \(1 -2=1=odd\). Thus \(x\) must be odd. In this case all its factors will be odd and the difference of any two distinct positive factors of \(x\) will be even. Sufficient.
Answer: D
Is positive integer \(x\) odd?
(1) The product of any two distinct positive factors of \(x\) is odd.
\(x\) cannot be even because if it is then it has 1 and 2 as factors and \(1*2=2=even\). Thus \(x\) must be odd. In this case all its factors will be odd and the product of any two distinct positive factors of \(x\) will be odd. Sufficient.
(2) The difference of any two distinct positive factors of \(x\) is even.
\(x\) cannot be even because if it is then it has 1 and 2 as factors and \(1 -2=1=odd\). Thus \(x\) must be odd. In this case all its factors will be odd and the difference of any two distinct positive factors of \(x\) will be even. Sufficient.
Answer: D
16 May 2024, 01:11
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