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16 Sep 2014, 01:08
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If \(n\) is a two-digit positive integer, what is the value of its tens digit?
(1) \(2n\) is a two-digit integer with a tens digit of 7.
(2) The tens digit of \((n - 9)\) is 2.
(1) \(2n\) is a two-digit integer with a tens digit of 7.
(2) The tens digit of \((n - 9)\) is 2.
16 Sep 2014, 01:08
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Official Solution:
If \(n\) is a two-digit positive integer, what is the value of its tens digit?
(1) \(2n\) is a two-digit integer with a tens digit of 7.
Since \(2n\) must be even, the above implies that \(2n\) can be any of the five numbers: 70, 72, 74, 76, or 78. Therefore, \(n\) can be 35, 36, 37, 38, or 39. In any of these cases, the tens digit of \(n\) is 3. Sufficient.
(2) The tens digit of \((n - 9)\) is 2.
\((n - 9)\) can be any of the numbers from 20 to 29, inclusive. Therefore, \(n\) can be any of the numbers from 29 to 38, inclusive. This means that the tens digit of \(n\) can be either 2 or 3. Not sufficient.
Answer: A
If \(n\) is a two-digit positive integer, what is the value of its tens digit?
(1) \(2n\) is a two-digit integer with a tens digit of 7.
Since \(2n\) must be even, the above implies that \(2n\) can be any of the five numbers: 70, 72, 74, 76, or 78. Therefore, \(n\) can be 35, 36, 37, 38, or 39. In any of these cases, the tens digit of \(n\) is 3. Sufficient.
(2) The tens digit of \((n - 9)\) is 2.
\((n - 9)\) can be any of the numbers from 20 to 29, inclusive. Therefore, \(n\) can be any of the numbers from 29 to 38, inclusive. This means that the tens digit of \(n\) can be either 2 or 3. Not sufficient.
Answer: A
19 Jan 2023, 05:34
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I think this is a high-quality question and I agree with explanation.
