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18 Oct 2021, 05:01
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Is a two digit positive integer \(xy\), where \(x\) is the tens digit and \(y\) is the units digits, even?
(1) \(x\) is an even number
(2) The greatest common factor of \(x\) and \(y\) is 1
(1) \(x\) is an even number
(2) The greatest common factor of \(x\) and \(y\) is 1
18 Oct 2021, 05:01
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Official Solution:
Is a two digit positive integer \(xy\), where \(x\) is the tens digit and \(y\) is the units digits, even?
Notice that the question asks whether \(y\), the units digit of a two digit positive integer \(xy\), is even.
(1) \(x\) is an even number. Clearly insufficient.
(2) The greatest common factor of \(x\) and \(y\) is 1
Also, insufficient. For example, consider 12 and 13.
(1)+(2) Both \(x\) and \(y\) cannot be even because in this case the greatest common factor of \(x\) and \(y\) would not be 1 (as given in the second statement), thus \(y\) is odd. Sufficient.
Answer: C
Is a two digit positive integer \(xy\), where \(x\) is the tens digit and \(y\) is the units digits, even?
Notice that the question asks whether \(y\), the units digit of a two digit positive integer \(xy\), is even.
(1) \(x\) is an even number. Clearly insufficient.
(2) The greatest common factor of \(x\) and \(y\) is 1
Also, insufficient. For example, consider 12 and 13.
(1)+(2) Both \(x\) and \(y\) cannot be even because in this case the greatest common factor of \(x\) and \(y\) would not be 1 (as given in the second statement), thus \(y\) is odd. Sufficient.
Answer: C
