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11 Feb 2023, 03:00
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
52% (02:40) correct
48%
(02:42)
wrong
based on 65
sessions
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Not Attempted Yet
If |x| ≠ |y| ≠ 0, is \(\frac{x^2}{x^2 - y^2} > \frac{y^2 - x^2}{y^2}\) ?
(1) \(|x - y| > 1\)
(2) \(|x| < |y| \)
(1) \(|x - y| > 1\)
(2) \(|x| < |y| \)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
12 Feb 2023, 09:25
Kudos
Bookmarks
Bunuel
Let's try to solve the premise first
\(\frac{x^2}{x^2 - y^2} > \frac{y^2 - x^2}{y^2}\)
\(\frac{x^2}{x^2 - y^2} - \frac{y^2 - x^2}{y^2} > 0\)
\(\frac{x^2}{x^2 - y^2} + \frac{x^2 - y^2}{y^2} > 0\)
\(\frac{ x^2y^2 + (x^2 -y^2)^2}{ (x^2 - y^2)y^2} > 0\)
Note all the terms except \((x^2 - y^2)\) is positive in this case.
Hence, for the expression to hold true \(x^2 - y^2 > 0\)
Taking square root on both sides
|x| > |y|
Hence, we need to find if |x| > |y|
Statement 1
(1) |x−y|>1
Case 1
-------- x --------- y -------- 0 -------
Ex: x = -100 | y = -1
|x| > |y| -- Yes !
Case 2
--------- y -------- 0 - x -----
Ex: x = 1 | y = -100
|x| > |y| -- No !
This statement is not sufficient.
We can eliminate A and D.
Statement 2
(2) \(|x| < |y| \)
This statement provides us with a definite answer. Hence sufficient.
Option B
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