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07 Jul 2026, 08:00
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B
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Difficulty:
75%
(hard)
Question Stats:
68% (01:58) correct
32%
(02:21)
wrong
based on 329
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If \(|x-y|=y-x\), \(x \ne y\), and \(y<0\), what is the value of \(\frac{x}{|x|}+\frac{|-y|}{-y}+\frac{x-y}{|y-x|}+\frac{|xy|}{xy}\)?
A. -2
B. 0
C. 1
D. 2
E. 4
A. -2
B. 0
C. 1
D. 2
E. 4
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⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
07 Jul 2026, 09:00
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GMAT Club Official Solution:
If \(|x-y|=y-x\), \(x \ne y\), and \(y<0\), what is the value of \(\frac{x}{|x|}+\frac{|-y|}{-y}+\frac{x-y}{|y-x|}+\frac{|xy|}{xy}\)?
A. -2
B. 0
C. 1
D. 2
E. 4
Absolute value properties:
• When a <= 0, then |a| = -a.
• When a >= 0, then |a| = a.
Now, since \(|x-y|=y-x=-(x-y)\), we have \(x < y\) and since \(y < 0\), we have \(x < y < 0\).
Thus:
\(\frac{x}{|x|}=\frac{x}{-x}=-1\), since \(x<0\).
\(\frac{|-y|}{-y}= \frac{|y|}{-y} =\frac{-y}{-y}=1\), since \(y<0\).
\(\frac{x-y}{|y-x|}=\frac{x-y}{y-x}=-1\), since \(y-x>0\).
\(\frac{|xy|}{xy}=\frac{xy}{xy}=1\), since \(x<0\) and \(y<0\), so \(xy>0\).
Therefore, the expression equals:
\(-1+1-1+1=0\)
Answer: B.
If \(|x-y|=y-x\), \(x \ne y\), and \(y<0\), what is the value of \(\frac{x}{|x|}+\frac{|-y|}{-y}+\frac{x-y}{|y-x|}+\frac{|xy|}{xy}\)?
A. -2
B. 0
C. 1
D. 2
E. 4
Absolute value properties:
• When a <= 0, then |a| = -a.
• When a >= 0, then |a| = a.
Now, since \(|x-y|=y-x=-(x-y)\), we have \(x < y\) and since \(y < 0\), we have \(x < y < 0\).
Thus:
\(\frac{x}{|x|}=\frac{x}{-x}=-1\), since \(x<0\).
\(\frac{|-y|}{-y}= \frac{|y|}{-y} =\frac{-y}{-y}=1\), since \(y<0\).
\(\frac{x-y}{|y-x|}=\frac{x-y}{y-x}=-1\), since \(y-x>0\).
\(\frac{|xy|}{xy}=\frac{xy}{xy}=1\), since \(x<0\) and \(y<0\), so \(xy>0\).
Therefore, the expression equals:
\(-1+1-1+1=0\)
Answer: B.
General Discussion
07 Jul 2026, 08:10
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Case 1: x-y=y-x so 2x=2y
so x=y
Case 2: x-y=-(y-x) this is not solvablesince both sides cancel out each other
So x=y..assumin g a value, say -2
so \( (-2/2)+(2/2)+((-2+2)/|-2+2|))+((|-2*-2|)/(-2*-2)) \)
-1+1+0+1=1
Hence C is the answer
so x=y
Case 2: x-y=-(y-x) this is not solvablesince both sides cancel out each other
So x=y..assumin g a value, say -2
so \( (-2/2)+(2/2)+((-2+2)/|-2+2|))+((|-2*-2|)/(-2*-2)) \)
-1+1+0+1=1
Hence C is the answer
