For all distinct non-zero values of x and y, is x > y?
(1) x - y > -y
(2) 1/x>1/y
can somebody explain me the concept?
OA-E
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Inequality X and Y
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sandipgumtya
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DavidG@VeritasPrep
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Statement 1: adding y to both sides of x - y > -y, gives us x > 0. Tells us nothing about y. Not Sufficient.For all distinct non-zero values of x and y, is x > y?
(1) x - y > -y
(2) 1/x>1/y
Statement 2: pick some easy numbers. If x = 2 and y = 3, we satisfy the condition, because 1/2 > 1/3. And the answer to the question is NO, x is not bigger than y ,as 2 is not greater than 3.
If x = 2 and y = -3, we satisfy the condition, because 1/2 > -(1/3). And the answer to the question is YES, x is bigger than y, as 2 is greater than -3.
Because we can get a NO and a YES, this is not sufficient.
Together, also not sufficient. Both of the scenarios we used in statement 2 involved a positive x, so we can reuse those scenarios when testing the statements together. Because we can get a NO and a YES, together the statements are still not sufficient.
Answer is E
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sandipgumtya
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Hi sandipgumtya,
When there are variables in the denominators of fractions, you have to be careful about 'rewriting' the inequalities. The two variables could be both positive OR both negative OR one of each....
For example, if X and Y are both POSITIVE, then you could use...
X = 2, Y = 3
1/2 > 1/3
In this example, the answer to the question (Is X > Y?) is NO.
BUT, if X is positive and Y is NEGATIVE
X = 2 Y = -3
1/2 > -1/3
In this example, the answer to the question is YES.
With variables in the denominators, it's often a good move to just leave the variables there and TEST VALUES to prove whether there's a consistent result or not.
GMAT assassins aren't born, they're made,
Rich
When there are variables in the denominators of fractions, you have to be careful about 'rewriting' the inequalities. The two variables could be both positive OR both negative OR one of each....
For example, if X and Y are both POSITIVE, then you could use...
X = 2, Y = 3
1/2 > 1/3
In this example, the answer to the question (Is X > Y?) is NO.
BUT, if X is positive and Y is NEGATIVE
X = 2 Y = -3
1/2 > -1/3
In this example, the answer to the question is YES.
With variables in the denominators, it's often a good move to just leave the variables there and TEST VALUES to prove whether there's a consistent result or not.
GMAT assassins aren't born, they're made,
Rich
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DavidG@VeritasPrep
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- Joined: Wed Jan 14, 2015 8:25 am
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If we take the reciprocal of both sides of an inequality, we must flip the inequality sign if both sides of the inequality are positive or if both sides of the inequality are negative.can't we write the second eqn as Y>X.?is it wrong>I chose B because of this.
For example, 3 < 4, but 1/3 > 1/4
And -3 > -4, but -(1/3) < -(1/4)
However, if one side is positive and one side is negative, we do not flip the inequality sign when taking the reciprocal. 4 > -2, and 1/4 > -(1/2)
In this case, even when testing the statements together, we only know that x is positive. y could be positive or negative.
