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14 May 2018, 01:30
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Question Stats:
60% (01:41) correct
40%
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wrong
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If x and y are positive integers, is x odd?
(1) x - 2y is a prime number
(2) x + 2y is a prime number
M33-103
(1) x - 2y is a prime number
(2) x + 2y is a prime number
M33-103
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04 Jul 2019, 05:47
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If \(x\) and \(y\) are positive integers, is \(x\) odd?
(1) \(x - 2y\) is a prime number.
If \(x - 2y=even \ prime\), that is if \(x - 2y=2\), then \(x = even+2y=even+even=even\) (consider \(x=4\) and \(y=1\) as an example). However, if \(x - 2y=odd \ prime\), then \(x = odd+2y=odd+even=odd\) (consider \(x=5\) and \(y=1\) as an example). Not sufficient.
(2) \(x + 2y\) is a prime number.
Given that \(x\) and \(y\) are positive integers, it's impossible for \(x + 2y\) to equal 2, the only even prime number. This is because \(x + 2y = \{minimum \ 1\} + \{ minimum \ 2\} = \{minimum \ 3\} > 2\). Therefore, \(x + 2y\) must equal an \(odd \ prime\). In this case, \(x =odd \ prime-2y=odd-even=odd\). Sufficient.
Answer: B
(1) \(x - 2y\) is a prime number.
If \(x - 2y=even \ prime\), that is if \(x - 2y=2\), then \(x = even+2y=even+even=even\) (consider \(x=4\) and \(y=1\) as an example). However, if \(x - 2y=odd \ prime\), then \(x = odd+2y=odd+even=odd\) (consider \(x=5\) and \(y=1\) as an example). Not sufficient.
(2) \(x + 2y\) is a prime number.
Given that \(x\) and \(y\) are positive integers, it's impossible for \(x + 2y\) to equal 2, the only even prime number. This is because \(x + 2y = \{minimum \ 1\} + \{ minimum \ 2\} = \{minimum \ 3\} > 2\). Therefore, \(x + 2y\) must equal an \(odd \ prime\). In this case, \(x =odd \ prime-2y=odd-even=odd\). Sufficient.
Answer: B
General Discussion
14 May 2018, 01:41
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Bunuel
St1
Lets put in values:
X=7 and y=2 then X-2Y = 3 = prime, X is odd
X = 4 and Y=2 then X-2Y = 2 = prime, X is even
So Statement 1 is not sufficient.
St 2
Now as 2 is the only even prime number and we already have 2Y which is multiple of 2, so any even valve of X will result in event number which will not be a prime number.
Hence X for 2nd case has to be odd for X+2Y to be prime number
Statement 2 is sufficient
Answer: option B
