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16 Sep 2014, 00:25
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When positive integer \(p\) is divided by 7, the remainder is 2. Is \(p\) divisible by 8?
(1) \(p\) is divisible by 2 and 3
(2) \(p < 100\)
(1) \(p\) is divisible by 2 and 3
(2) \(p < 100\)
16 Sep 2014, 00:25
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Official Solution:
When positive integer \(p\) is divided by 7, the remainder is 2. Is \(p\) divisible by 8?
When a positive integer \(p\) is divided by 7, the remainder is 2 can be expressed as \(p=7q+2\), meaning that \(p\) can be: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, and so forth.
(1) \(p\) is divisible by 2 and 3.
This statement implies that \(p\) is a multiple of 6. Hence, \(p\) could be 30 (in which case the answer is NO) or 72 (in which case the answer is YES). This is not sufficient.
(2) \(p < 100\).
This statement is clearly insufficient by itself.
(1)+(2) Even when combining the two statements, \(p\) could still be either 30 (answer NO) or 72 (answer YES). Not sufficient.
Answer: E
When positive integer \(p\) is divided by 7, the remainder is 2. Is \(p\) divisible by 8?
When a positive integer \(p\) is divided by 7, the remainder is 2 can be expressed as \(p=7q+2\), meaning that \(p\) can be: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, and so forth.
(1) \(p\) is divisible by 2 and 3.
This statement implies that \(p\) is a multiple of 6. Hence, \(p\) could be 30 (in which case the answer is NO) or 72 (in which case the answer is YES). This is not sufficient.
(2) \(p < 100\).
This statement is clearly insufficient by itself.
(1)+(2) Even when combining the two statements, \(p\) could still be either 30 (answer NO) or 72 (answer YES). Not sufficient.
Answer: E
General Discussion
20 May 2023, 11:14
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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.
