If the units digit of the positive integer n is 5, what is the tens digit of n?
1) The tens digit of n + 5 is 7
2) The tens digit of n - 6 is 5
Statement 1:
Options for n+5:
70, 71, 72, 73, 74, 75, 76, 77, 78, 79
Subtracting 5 from each of the values in the list above, we get the following options for n:
65, 66, 67, 68, 69, 70, 71, 72, 73, 74
Of the resulting options for n, only 65 satisfies the constraint that n must have a units digit of 5, with the result that the tens digit of n is 6.
The same reasoning will apply if our list of options for n+5 is composed of integers with more than two digits (such as 170-179 or 270-279).
Thus, the tens digit of n must be 6.
SUFFICIENT.
Statement 2:
Options for n-6:
50, 51, 52, 53, 54, 55, 56, 57, 58, 59
Adding 6 to each of the values in the list above, we get the following options for n:
56, 57, 58, 59, 60, 61, 62, 63, 64, 65
Of the resulting options for n, only 65 satisfies the constraint that n must have a units digit of 5, with the result that the tens digit of n is 6.
The same reasoning will apply if our list of options for n-6 is composed of integers with more than two digits (such as 150-159 or 250-259).
Thus, the tens digit of n must be 6.
SUFFICIENT.
The correct answer is
D.
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