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If \(|\frac{x}{y}| = 1\), what is the value of \(|x| - |y|\) ?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
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04 May 2024, 08:15
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Official Solution:
If \(|\frac{x}{y}| = 1\), what is the value of \(|x| - |y|\) ?
A. 0
B. 1
C. 2
D. 3
E. 4
Generally, \(|\frac{a}{b}| = \frac{|a|}{|b|}\). Hence, we are given that \(\frac{|x|}{|y|} = 1\), from which it follows that \(|x| = |y|\). Therefore, \(|x| - |y| = |x| - |x| = 0\).
Answer: A
If \(|\frac{x}{y}| = 1\), what is the value of \(|x| - |y|\) ?
A. 0
B. 1
C. 2
D. 3
E. 4
Generally, \(|\frac{a}{b}| = \frac{|a|}{|b|}\). Hence, we are given that \(\frac{|x|}{|y|} = 1\), from which it follows that \(|x| = |y|\). Therefore, \(|x| - |y| = |x| - |x| = 0\).
Answer: A
General Discussion
21 Apr 2024, 11:18
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Bunuel
If \(|\frac{x}{y}| = 1\), what is the value of \(|x| - |y|\) ?
A. 0
B. 1
C. 2
D. 3
E. 4
\(|\frac{x}{y}| = 1\) → Indicates the magnitude of x and y is the same.A. 0
B. 1
C. 2
D. 3
E. 4
Hence, \(x\) and \(y\) can represent the same point on a number line, or \(x\) and \(y\) can lie on opposite sides of zero. However, the distance of \(x\) from 0 will be equal to the distance of \(y\) from 0.
|x| → Represents the distance of point \(x\) from 0.
|y| → Represents the distance of point \(y\) from 0.
As the distance of point \(x\) from 0 equals the distance of point \(y\) from 0, |x| - |y| will always be equal to 0
Option A
