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In Episode 4 of our GMAT Ninja CR series, we tackle the most intimidating CR question type: Boldface & "Legalese" questions. If you've ever stared at an answer choice that reads, "The first is a consideration introduced to counter a position that...
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27 Apr 2023, 13:47
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27 Apr 2023, 13:47
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Official Solution:
Is \(|x - y| = ||x| - |y||\)?
(1) \(xy > 0\)
This statement implies that \(x\) and \(y\) have the same sign.
If both are positive, \(|x| = x\) and \(|y| = y\), and the question becomes: is \(|x - y| = |x - y|\)? The answer to this question is YES.
If both are negative, \(|x| = -x\) and \(|y| = -y\), and the question becomes: is \(|x - y| = |-x + y|\)? This can be rewritten as: is \(|x - y| = |y - x|\)? Since both \(|x - y|\) and \(|y - x|\) represent the distance between points \(x\) and \(y\) on the number line, they are equal and the answer to this question is once again YES.
Sufficient.
(2) \(x < y < 0\)
This statement implies that both \(x\) and \(y\) are negative. Similarly, as above, the question becomes: is \(|x - y| = |y - x|\)? The answer to this question is YES. Sufficient.
Answer: D
Is \(|x - y| = ||x| - |y||\)?
(1) \(xy > 0\)
This statement implies that \(x\) and \(y\) have the same sign.
If both are positive, \(|x| = x\) and \(|y| = y\), and the question becomes: is \(|x - y| = |x - y|\)? The answer to this question is YES.
If both are negative, \(|x| = -x\) and \(|y| = -y\), and the question becomes: is \(|x - y| = |-x + y|\)? This can be rewritten as: is \(|x - y| = |y - x|\)? Since both \(|x - y|\) and \(|y - x|\) represent the distance between points \(x\) and \(y\) on the number line, they are equal and the answer to this question is once again YES.
Sufficient.
(2) \(x < y < 0\)
This statement implies that both \(x\) and \(y\) are negative. Similarly, as above, the question becomes: is \(|x - y| = |y - x|\)? The answer to this question is YES. Sufficient.
Answer: D
