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16 Sep 2014, 00:43
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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) Both \(x\) and \(y\) are less than 5.
(1) \(x + y\) is a prime number.
(2) Both \(x\) and \(y\) are less than 5.
16 Sep 2014, 00:43
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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.
This information is insufficient to determine the value of \(|x - y|\). For example, consider \(x = 3\), \(y = 2\) and \(x = 5\), \(y = 2\).
(2) Both \(x\) and \(y\) are less than 5.
There are two prime numbers less than 5, which are 2 and 3. If \(x = 3\) and \(y = 2\), or vice versa, \(|x - y| = 1\). However, if \(x = 2\), and \(y = 2\), or if \(x = 3\) and \(y = 3\), \(|x - y| = 0\). Not sufficient. Note that in the GMAT, unless explicitly stated otherwise, different variables CAN represent the same number. So, \(x = y\) is a valid scenario.
(1)+(2) For the sum of two prime numbers, each less than 5, to be a prime, one must be 2 and the other must be 3. Hence, either \(x = 3\) and \(y = 2\) or vice versa. In any case, \(|x - y| = 1\). Sufficient.
Answer: C
If \(x\) and \(y\) are prime numbers, what is the value of \(|x - y|\)?
(1) \(x + y\) is a prime number.
This information is insufficient to determine the value of \(|x - y|\). For example, consider \(x = 3\), \(y = 2\) and \(x = 5\), \(y = 2\).
(2) Both \(x\) and \(y\) are less than 5.
There are two prime numbers less than 5, which are 2 and 3. If \(x = 3\) and \(y = 2\), or vice versa, \(|x - y| = 1\). However, if \(x = 2\), and \(y = 2\), or if \(x = 3\) and \(y = 3\), \(|x - y| = 0\). Not sufficient. Note that in the GMAT, unless explicitly stated otherwise, different variables CAN represent the same number. So, \(x = y\) is a valid scenario.
(1)+(2) For the sum of two prime numbers, each less than 5, to be a prime, one must be 2 and the other must be 3. Hence, either \(x = 3\) and \(y = 2\) or vice versa. In any case, \(|x - y| = 1\). Sufficient.
Answer: C
General Discussion
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21 Jun 2017, 06:35
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I think this is a high-quality question and I agree with explanation.
