If x and y are non-zero integers, is x divisible by 11?
(1) 2x+8 = 3y (2) 6y-5 is divisible by 11
(1) 2x+8 = 3y (2) 6y-5 is divisible by 11
Hi carlos.lara.7,
This question can be solved by TESTing VALUES, but it involves a relatively rare Number Property that most Test Takers would not recognize. We're told that X and Y are NON-ZERO INTEGERS. We're asked if X is divisible by 11. This is a YES/NO question.
1) 2X + 8 = 3Y
IF...
X = 2, Y = 4
then the answer to the question is NO
IF...
X = 11, Y = 10
then the answer to the question is YES
Fact 1 is INSUFFICIENT
2) 6Y - 5 is divisible by 11.
This tells us NOTHING about X.
Fact 2 is INSUFFICIENT
Combined, we know.
2X + 8 = 3Y
6Y - 5 is divisible by 11.
Notice how Fact 1 uses '3Y' and Fact 2 uses '6Y' - we can combine those facts. First we 'double' the first equation...
4X + 16 = 6Y
6Y - 5 = positive multiple of 11
4X + 16 - 5 = positive multiple of 11
4X + 11 = positive multiple of 11
Since we're adding two terms together, and one of the terms (the '11') is a multiple of 11, for the SUM to be a multiple of 11 the OTHER term (the "4X") must ALSO be a multiple of 11. Since X is an integer, the only way for 4X to a multiple of 11 is if X itself is a multiple of 11. Under these conditions, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
Sufficient.
