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16 Sep 2014, 00:18
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If \(n\) is a positive two-digit number divisible by 3, is \(n\) less than 50?
(1) The sum of the digits of \(n\) is a multiple of 18.
(2) The product of the digits of \(n\) is a multiple of 9.
(1) The sum of the digits of \(n\) is a multiple of 18.
(2) The product of the digits of \(n\) is a multiple of 9.
16 Sep 2014, 00:18
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Official Solution:
If \(n\) is a positive two-digit number divisible by 3, is \(n\) less than 50?
(1) The sum of the digits of \(n\) is a multiple of 18.
The only two-digit number with a digit sum that is a multiple of 18 is 99. This means \(n\) is not less than 50. Sufficient.
(2) The product of the digits of \(n\) is a multiple of 9.
There are several two-digit numbers that satisfy this. For instance, if \(n=36\) (\(3 * 6 = 18\), which is a multiple of 9), the answer is YES. But if \(n=99\) (\(9 * 9 = 81\), also a multiple of 9), the answer is NO. Therefore, statement (2) is not sufficient to determine if \(n\) is less than 50.
Answer: A
If \(n\) is a positive two-digit number divisible by 3, is \(n\) less than 50?
(1) The sum of the digits of \(n\) is a multiple of 18.
The only two-digit number with a digit sum that is a multiple of 18 is 99. This means \(n\) is not less than 50. Sufficient.
(2) The product of the digits of \(n\) is a multiple of 9.
There are several two-digit numbers that satisfy this. For instance, if \(n=36\) (\(3 * 6 = 18\), which is a multiple of 9), the answer is YES. But if \(n=99\) (\(9 * 9 = 81\), also a multiple of 9), the answer is NO. Therefore, statement (2) is not sufficient to determine if \(n\) is less than 50.
Answer: A
General Discussion
10 Sep 2023, 10:39
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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.
