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16 Sep 2014, 00:46
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If \(p\) is a positive integer, what is the remainder when \(p^2\) is divided by 12?
(1) \(p\) is odd number
(2) \(p\) is prime number
(1) \(p\) is odd number
(2) \(p\) is prime number
16 Sep 2014, 00:46
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Official Solution:
If \(p\) is a positive integer, what is the remainder when \(p^2\) is divided by 12?
(1) \(p\) is an odd number.
If \(p=1\), the remainder when \(p^2\) is divided by 12 is 1. However, if \(p=3\), the remainder when \(p^2\) is divided by 12 is 9. Not sufficient.
(2) \(p\) is a prime number.
If \(p=3\), the remainder when \(p^2\) is divided by 12 is 9. However, if \(p=5\), the remainder when \(p^2\) is divided by 12 is 1. Not sufficient.
(1)+(2) The values of \(p\) used in statement (2) were both odd and thus satisfy statement (1). So, if \(p=3\), the remainder when \(p^2\) is divided by 12 is 9. However, if \(p=5\), the remainder when \(p^2\) is divided by 12 is 1. Not sufficient.
Answer: E
If \(p\) is a positive integer, what is the remainder when \(p^2\) is divided by 12?
(1) \(p\) is an odd number.
If \(p=1\), the remainder when \(p^2\) is divided by 12 is 1. However, if \(p=3\), the remainder when \(p^2\) is divided by 12 is 9. Not sufficient.
(2) \(p\) is a prime number.
If \(p=3\), the remainder when \(p^2\) is divided by 12 is 9. However, if \(p=5\), the remainder when \(p^2\) is divided by 12 is 1. Not sufficient.
(1)+(2) The values of \(p\) used in statement (2) were both odd and thus satisfy statement (1). So, if \(p=3\), the remainder when \(p^2\) is divided by 12 is 9. However, if \(p=5\), the remainder when \(p^2\) is divided by 12 is 1. Not sufficient.
Answer: E
22 Jun 2018, 11:45
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I think this is a high-quality question and I agree with explanation.
