BTGmoderatorDC wrote:Is the tens digit of a two digit integer k divisible by 3?
(1) k-5 is a multiple of 3
(2) k-11 is a multiple of 3
OA E
Source: Manhattan GMAT
Rephrased question:
is the tens digit of k a 3, 6, or 9?
Test values with the statement to try to prove insufficiency:
(1) k - 5 is a multiple of 3
This tells us that k is 5 more than some multiple of 3. Test some 2-digit multiples of 3:
Case 1: 3x = 27 --> k = 32.
Is the tens digit a multiple of 3? Yes.
Case 1: 3x = 42 --> k = 47.
Is the tens digit a multiple of 3? No.
Insufficient.
(2) k - 11 is a multiple of 3
This tells us that k is 11 more than some multiple of 3. Test some 2-digit multiples of 3:
Case 1: 3x = 27 --> k = 38.
Is the tens digit a multiple of 3? Yes.
Case 1: 3x = 42 --> k = 53.
Is the tens digit a multiple of 3? No.
Insufficient.
(1) & (2) Together
k is a number that is 5 more than some multiple of 3, and also 11 more than a multiple of 3. But since 5 and 11 are 6 apart, any given number that's 5 more than a multiple of 3 will also be 11 more than some other multiple of 3:
38: 5 more than 33, 11 more than 27
53: 5 more than 48, 11 more than 42.
Since we can come up with a value for k in the 30s and one in the 50s that fit both statements, we don't have enough to answer the question.
The answer is
E.
