Hi barksdale,

We're told that X and Y are INTEGERS and that X > 0. We're asked if Y > 0. This is a YES/NO question. We can solve it by TESTing VALUES.

1) 7X - 2Y > 0

IF....
X = 10, Y = 1
Then the answer to the question is YES.

X = 10, Y = -1
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) -Y < X

The same two TESTs that I used in Fact 1 also 'fit' Fact 2...

IF....
X = 10, Y = 1
Then the answer to the question is YES.

X = 10, Y = -1
Then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that fit Fact 1 and Fact 2 and product two different answers (one YES and one NO).
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

barksdale wrote:If x and y are integers and x > 0, is y > 0?

(1) 7x - 2y > 0
(2) -y < x

What is the process we use to know the answer is D?

Statement 1: 7x - 2y > 0

=> 3.5|x| > y

Say x = 1, then for y = 3, 2 or 1, the answer is YES, y > 0. However, if y = 0 or a negative integer, the answer is NO, y is not greater than 0.

Statement 2: -y < x

=> -y < |x|

If y = Any positive integer, the answer is YES, y > 0. However, if y = 0 or one among few qualified positive integers (depending on the value of x), the answer is NO, y is not greater than 0.

Statement 1 and 2:

The cases discussed in statement 1 qualify in statement 2 also, thus, even combining both the statement would not suffice.

The correct answer: E

Hope this helps!

-Jay
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barksdale wrote:If x and y are integers and x > 0, is y > 0?

(1) 7x - 2y > 0
(2) -y < x

What is the process we use to know the answer is D?

You must have made a typo, or misread the answer key for this one. As the others have demonstrated, the correct answer is actually E, not D.

Here's a slightly different interpretation of the statements:

(1) 7x - 2y > 0
Rearrange:
7x > 2y
x > (2/7)y
So x is greater than some fraction of y... that could be true if y was some positive numbers, or if y was any negative number. Insufficient to tell us whether y is positive.

(2) -y < x
Rearrange:
x > -y
This could mean that y is any positive number - since x is positive, it will always be greater than -1 * any positive. Or y could be 0, or a negative with a smaller absolute value than x. Insufficient.

(1 & 2)
We can combine the inequalities algebraically:
x > (2/7)y
+ x > -y
-------------
2x > -(5/7)y
x > -(5/14)y

Once again, this could be true for certain positive values and certain negative values of y. Insufficient.

barksdale wrote:If x and y are integers and x > 0, is y > 0?

(1) 7x - 2y > 0
(2) -y < x

Target question: Is y > 0

Given: x and y are integers and x > 0

Statement 1: 7x - 2y > 0
Add 2y to both sides to get: 7x > 2y
Divide both sides by 2 to get: 7x/2 > y
So, y is less than 7x/2. Since we only know that x is a positive integer, this probably isn't enough information to answer the target question.
Let's TEST some values.
If x = 2, then 7x/2 = (7)(2)/2 = 7, which means y is less than 7.
Well, it could be the case that y = 1 (in which case y > 0), or it could be the case that y = -1 (in which case y < 0)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: -y < x
Rearrange to get: y > -x
Since we only know that x is a positive integer, this probably isn't enough information to answer the target question.
Let's TEST some values.
If x = 2, then -x = -2, which means y is greater than -2.
Well, it could be the case that y = 1 (in which case y > 0), or it could be the case that y = -1 (in which case y < 0)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent