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
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
