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?
If x and y are integers
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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
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
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Statement 1: 7x - 2y > 0barksdale 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?
=> 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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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.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?
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.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Target question: Is y > 0barksdale wrote:If x and y are integers and x > 0, is y > 0?
(1) 7x - 2y > 0
(2) -y < x
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