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18 Jul 2018, 02:37
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:42) correct
36%
(01:58)
wrong
based on 442
sessions
History
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Not Attempted Yet
GMAT CLUB TESTS' FRESH QUESTION
If \(z ≠ 0\), is \(x = y\) ?
(1) \(xy + \frac{1}{|z|} = 0\)
(2) \(\frac{x}{y} + z^2 = 0\)
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08 Nov 2021, 10:22
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Bunuel
Official Solution:
If \(z ≠ 0\), is \(x = y\) ?
(1) \(xy + \frac{1}{|z|} = 0\)
Re-arrange: \(\frac{1}{|z|}=-xy\)
Now, the left hand side is an absolute value, which is positive, so \(-xy\) must also be positive.
\(-xy > 0\);
\(xy < 0\). \(x\) and \(y\) have the opposite signs, so \(x \neq y\). Sufficient.
(2) \(\frac{x}{y} + z^2 = 0\)
Re-arrange: \(z^2=-\frac{x}{y}\)
Now, the left hand side is the square of an integer, which is positive, so \(-\frac{x}{y}\) must also be positive.
\(-\frac{x}{y} > 0\);
\(\frac{x}{y} < 0\). \(x\) and \(y\) have the opposite signs, so \(x \neq y\). Sufficient.
Answer: D
General Discussion
18 Jul 2018, 03:56
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from a we know that xy = negative number, as 1/|x| is 1/ positive. Therefore, x and y are of the opposite signs.
same applies for statement b, as x^2 is always positive
same applies for statement b, as x^2 is always positive
