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If n is an integer between 10 and 100, is the tens digit of

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Source: — Data Sufficiency |

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by ceilidh.erickson » Mon Aug 20, 2018 1:40 pm

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BTGmoderatorDC wrote:If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

(2) The only prime factor of n is 3.

OA D

Source: Manhattan GMAT
For digit questions in DS, the best strategy is often to test values.

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

This tells us that either n must be a multiple of 20 (multiple of both 4 and 5), or some multiple of 20 + 1, +2, or +3 (if we add 4 we'll hit another multiple of 4 but not of 5, and the remainders thereafter won't be the same). So, we can express the possible values of n as:
[20x, 20x + 1, 20x + 2, 20x + 3] where x is some integer.
For any of these, 20x will give us a tens digit of 2, 4, 6, or 8. The tens digit must be even. Sufficient.

(2) The only prime factor of n is 3.

Translation: n must be a power of 3. List out the powers of 3:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243

The only values between 10 and 100 are 27 and 81, both of which have an even tens digit. Sufficient.

The answer is D.
Ceilidh Erickson
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Harvard Graduate School of Education
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by fskilnik@GMATH » Mon Aug 20, 2018 2:29 pm

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If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

(2) The only prime factor of n is 3.
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Good problem.
The solution above follows the notations and rationale taught in the <b>GMATH</b> method.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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