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16 Sep 2014, 01:09
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What is the remainder when a positive integer \(p\) is divided by 2?
(1) \(p\) is a prime number/
(2) \(p \gt 10\).
(1) \(p\) is a prime number/
(2) \(p \gt 10\).
16 Sep 2014, 01:09
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Official Solution:
What is the remainder when a positive integer \(p\) is divided by 2?
Recall that a positive integer, when divided by 2, can only yield two possible remainders: 0 (if the integer is even) or 1 (if the integer is odd). Essentially, the question is asking whether \(p\) is even or odd.
(1) \(p\) is a prime number.
\(p\) might be 2, which is even, or another prime such as 3, which is odd. Therefore, this is not sufficient.
(2) \(p \gt 10\).
This information is clearly insufficient on its own.
(1)+(2) Any prime number greater than 10 is odd. Hence, it leaves a remainder of 1 when divided by 2. Sufficient.
Answer: C
What is the remainder when a positive integer \(p\) is divided by 2?
Recall that a positive integer, when divided by 2, can only yield two possible remainders: 0 (if the integer is even) or 1 (if the integer is odd). Essentially, the question is asking whether \(p\) is even or odd.
(1) \(p\) is a prime number.
\(p\) might be 2, which is even, or another prime such as 3, which is odd. Therefore, this is not sufficient.
(2) \(p \gt 10\).
This information is clearly insufficient on its own.
(1)+(2) Any prime number greater than 10 is odd. Hence, it leaves a remainder of 1 when divided by 2. Sufficient.
Answer: C
23 Oct 2023, 10:44
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
