If x and y are non-zero integers, is 3x greater than 2y?

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If x and y are non-zero integers, is 3x greater than 2y?

(1) The ratio of x to y is more than 1/2.
(2) The sum of x and y is less than 0.

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by GMATGuruNY » Sat Mar 11, 2017 6:02 am
Mo2men wrote:If x and y are non-zero integers, is 3x greater than 2y?

(1) The ratio of x to y is more than 1/2.
(2) The sum of x and y is less than 0.
On the GMAT, the term ratio is constrained to POSITIVE VALUES.
Feel free to ignore this problem.
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by [email protected] » Sat Mar 11, 2017 11:10 am
HI Mo2men,

Mitch brings up a good point. We can change the prompt a bit (by rewording Fact 1) to create a prompt more in line with what you might see on the GMAT:

If X and Y are non-zero integers, is 3x greater than 2y?

(1) X/Y > 1/2.
(2) The sum of X and Y is less than 0.

This is a YES/NO question. It can be solved by TESTing VALUES.

(1) X/Y > 1/2.

This Fact tells us that X and Y are either both positive OR both negative.

IF....
X = 2, Y = 1... then the answer to the question is YES
X = -2, Y = -1... then the answer to the question is NO
Fact 1 is INSUFFICIENT

(2) The sum of X and Y is less than 0.

IF....
X = -2, Y = -4... then the answer to the question is YES
X = -2, Y = -1... then the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we already have one TEST that 'fits' both Facts...

IF....
X = -3, Y = -5... then the answer to the question is YES
X = -2, Y = -1... then the answer to the question is NO
Combined, INSUFFICIENT

Final Answer: E

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