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16 Sep 2014, 00:16
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If \(x\) is a positive integer, is \(x\) a prime number?
(1) \(x\) is a multiple of a prime number.
(2) \(x=a*b\), where \(a\) and \(b\) are different integers.
(1) \(x\) is a multiple of a prime number.
(2) \(x=a*b\), where \(a\) and \(b\) are different integers.
16 Sep 2014, 00:16
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Official Solution:
If \(x\) is a positive integer, then is \(x\) a prime number?
(1) \(x\) is a multiple of a prime number.
If \(x=2\), then the answer is YES, as every integer is a multiple of itself. However, if \(x=4\), the answer is Not Sufficient.
(2) \(x=a*b\), where \(a\) and \(b\) are different integers.
Any integer greater than 1 can indeed be expressed as the product of two different integers. For instance, \(x=2\) (which is prime) can be written as \(1*2\), and \(x=4\) (which is not prime) can be written as \(1*4\). Not sufficient.
(1)+(2) From (2) we deduce that \(x\) is not 1, but this does not help us determine whether \(x\) is prime. For example, if \(x=2\), the answer would be YES, but if \(x=4\), the answer would be NO. Not sufficient.
Answer: E
If \(x\) is a positive integer, then is \(x\) a prime number?
(1) \(x\) is a multiple of a prime number.
If \(x=2\), then the answer is YES, as every integer is a multiple of itself. However, if \(x=4\), the answer is Not Sufficient.
(2) \(x=a*b\), where \(a\) and \(b\) are different integers.
Any integer greater than 1 can indeed be expressed as the product of two different integers. For instance, \(x=2\) (which is prime) can be written as \(1*2\), and \(x=4\) (which is not prime) can be written as \(1*4\). Not sufficient.
(1)+(2) From (2) we deduce that \(x\) is not 1, but this does not help us determine whether \(x\) is prime. For example, if \(x=2\), the answer would be YES, but if \(x=4\), the answer would be NO. Not sufficient.
Answer: E
General Discussion
24 Feb 2023, 13:54
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
