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16 Sep 2014, 01:27
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If \(a\) and \(b\) are integers and \(ab=2\), is \(a=2\)?
(1) \(b+3\) is not a prime number
(2) \(a \gt b\)
(1) \(b+3\) is not a prime number
(2) \(a \gt b\)
16 Sep 2014, 01:27
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Official Solution:
If \(a\) and \(b\) are integers and \(ab=2\), is \(a=2\)?
Note that we are not given that \(a\) and \(b\) are positive integers.
The possible integer pairs for \((a, b)\) that satisfy \(ab=2\) are: (1, 2), (-1, -2), (2, 1), and (-2, -1). Essentially, we are examining whether we have the third case, where \(a=2\) and \(b=1\).
(1) \(b+3\) is not a prime number.
This statement eliminates the 1st and 4th cases. However, the 2nd and 3rd cases still remain, so it is not sufficient to determine whether \(a=2\).
(2) \(a > b\).
This statement also eliminates the 1st and 4th options. Not sufficient.
(1)+(2) When combining both statements, there are still two possibilities: (-1, -2) and (2, 1). Not sufficient.
Answer: E
If \(a\) and \(b\) are integers and \(ab=2\), is \(a=2\)?
Note that we are not given that \(a\) and \(b\) are positive integers.
The possible integer pairs for \((a, b)\) that satisfy \(ab=2\) are: (1, 2), (-1, -2), (2, 1), and (-2, -1). Essentially, we are examining whether we have the third case, where \(a=2\) and \(b=1\).
(1) \(b+3\) is not a prime number.
This statement eliminates the 1st and 4th cases. However, the 2nd and 3rd cases still remain, so it is not sufficient to determine whether \(a=2\).
(2) \(a > b\).
This statement also eliminates the 1st and 4th options. Not sufficient.
(1)+(2) When combining both statements, there are still two possibilities: (-1, -2) and (2, 1). Not sufficient.
Answer: E
General Discussion
MsInvBanker
28 Sep 2018, 02:58
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I did not consider that the numbers could be both negatives. A mistake I need to avoid.
