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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.
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05 Nov 2018, 00:10
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B
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Difficulty:
25%
(medium)
Question Stats:
75% (01:06) correct
25%
(01:23)
wrong
based on 114
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Not Attempted Yet
If each of w, x, y and z are positive numbers, is \(\frac{w}{x}*\frac{y}{z} > \frac{y}{x}\) ?
(1) y > x
(2) w > z
(1) y > x
(2) w > z
05 Nov 2018, 01:14
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Bunuel
Note: All are positive integers.
Given ,
\(\frac{w}{x}*\frac{y}{z} > \frac{y}{x}\)
w/z >1
Statement 1: y>x. impertinent information .
Statement 2: w>z. in this case w/z >1.
18 Mar 2020, 08:25
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Bunuel
Given: w, x, y and z are positive numbers,
Target question: Is \((\frac{w}{x})(\frac{y}{z}) > \frac{y}{x}\)?
This is a good candidate for rephrasing the target question
Take: \((\frac{w}{x})(\frac{y}{z}) > \frac{y}{x}\)
Simplify: \(\frac{wy}{xz} > \frac{y}{x}\)
Since \(x\) is POSITIVE, we can safely multiply both sides of the inequality by \(x\) to get: \(\frac{wy}{z} > y\)
Likewise, since \(z\) is POSITIVE, we can multiply both sides \(z\) to get: \(wy > yz\)
Finally, since \(y\) is POSITIVE, we can divide both sides \(y\) to get: \(w > z\)
REPHRASED target question: Is \( w> z\) ?
Aside: the video below has tips on rephrasing the target question
Statement 1: y > x
Since statement 1 provides no information about w and z, there is no way to answer the REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT
Statement 2: w > z
Perfect! The answer to the REPHRASED target question is YES, w is greater than z
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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