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16 Sep 2014, 01:23
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If \(x\) and \(y\) are prime numbers, what is the value of \(x+y\) ?
(1) \(x - y\) is a prime number.
(2) \(y \lt x \lt 6\)
(1) \(x - y\) is a prime number.
(2) \(y \lt x \lt 6\)
16 Sep 2014, 01:23
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Official Solution:
If \(x\) and \(y\) are prime numbers, what is the value of \(x+y\)?
(1) \(x-y\) is a prime number.
If \(x=5\) and \(y=2\) (notice that in this case \(x-y=3\), which is prime), then \(x+y=7\). But if \(x=5\) and \(y=3\) (notice that in this case \(x-y=2\), which is prime), then \(x+y=8\). Not sufficient.
(2) \(y \lt x \lt 6\).
The same example from the first statement applies here as well. Thus, it's not sufficient.
(1)+(2) Again, the example from statement (1) is still valid and gives two different values for \(x+y\). Not sufficient.
Answer: E
If \(x\) and \(y\) are prime numbers, what is the value of \(x+y\)?
(1) \(x-y\) is a prime number.
If \(x=5\) and \(y=2\) (notice that in this case \(x-y=3\), which is prime), then \(x+y=7\). But if \(x=5\) and \(y=3\) (notice that in this case \(x-y=2\), which is prime), then \(x+y=8\). Not sufficient.
(2) \(y \lt x \lt 6\).
The same example from the first statement applies here as well. Thus, it's not sufficient.
(1)+(2) Again, the example from statement (1) is still valid and gives two different values for \(x+y\). Not sufficient.
Answer: E
24 Aug 2023, 13:03
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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.
