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16 Sep 2014, 00:16
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If \(ab\) represents a two-digit positive integer, where \(a\) is the tens digit and \(b\) is the units digit, what is the value of \(ab\)?
(1) \(a + b = 4\)
(2) \(a - b = 2\)
(1) \(a + b = 4\)
(2) \(a - b = 2\)
16 Sep 2014, 00:16
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Official Solution:
If \(ab\) represents a two-digit positive integer, where \(a\) is the tens digit and \(b\) is the units digit, what is the value of \(ab\)?
(1) \(a + b = 4\)
From the equation above, \(ab\) could be 40, 31, 22, or 13. Thus, it's insufficient.
(2) \(a - b = 2\)
From this equation, potential values for \(ab\) include 20, 31, 42, 53, 64, 75, 86, or 97. Hence, it's also insufficient.
(1)+(2) We have two distinct linear equations. By solving for each variable, we find that the two-digit number \(ab = 31\). Sufficient.
Answer: C
If \(ab\) represents a two-digit positive integer, where \(a\) is the tens digit and \(b\) is the units digit, what is the value of \(ab\)?
(1) \(a + b = 4\)
From the equation above, \(ab\) could be 40, 31, 22, or 13. Thus, it's insufficient.
(2) \(a - b = 2\)
From this equation, potential values for \(ab\) include 20, 31, 42, 53, 64, 75, 86, or 97. Hence, it's also insufficient.
(1)+(2) We have two distinct linear equations. By solving for each variable, we find that the two-digit number \(ab = 31\). Sufficient.
Answer: C
18 Oct 2023, 09:54
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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.
