GMAT Exam pack 2 - DS - Number properties

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GMAT Exam pack 2 - DS - Number properties

by lucas211 » Fri Jun 24, 2016 3:31 am
Hello BTG

Would appreciate a little help on the following question.

Thanks in advance
Lucas
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by GMATGuruNY » Fri Jun 24, 2016 3:57 am
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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by ceilidh.erickson » Fri Jun 24, 2016 10:02 am
Alternatively, we could think about this one conceptually:

1) If n has a units digit of 5, then n + 5 will have a units digit of 0, and the tens digit will shift up one digit:
Image

Image

If the tens digit of n+5 is 7, n+5 must be 70, and n must be 65. Sufficient.

2) If n has a units digit of 5, then n - 6 will have a units digit of 9, and the tens digit will shift down one digit:

Image

If the tens digit of n-6 is 5, n-6 must be 59, and n must be 65. Sufficient.
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