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23 May 2019, 21:40
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If \(x^2 - y^2 = 0\) and \(xy \neq 0\), which of the following MUST be true?
I. x = y
II. |x| = |y|
III. \(\frac{x^2}{y^2}=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
I. x = y
II. |x| = |y|
III. \(\frac{x^2}{y^2}=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
Rakesh1987
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Joined: 17 Jul 2018
Last visit: 27 Aug 2022
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Location: India
Concentration: Finance, Leadership
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GMAT 1: 760 Q50 V44
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Updated on: 23 May 2019, 22:52
Originally posted by Rakesh1987 on 23 May 2019, 22:02.
Last edited by Rakesh1987 on 23 May 2019, 22:52, edited 1 time in total.
Last edited by Rakesh1987 on 23 May 2019, 22:52, edited 1 time in total.
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Bunuel
If \(x^2 - y^2 = 0\) and \(xy \neq 0\), which of the following MUST be true?
I. x = y
II. |x| = |y|
III. \(\frac{x^2}{y^2}=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
I. x = y
II. |x| = |y|
III. \(\frac{x^2}{y^2}=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
\(x^2 - y^2 = 0\)
=> \(x^2=y^2\)
=> \(x=+-y\)
I. x = y. Not necessarily true as x can be equal to -y.
II. |x| = |y|. |x| = |y| means either x=y (which is same as -x=-y) or x=-y (which is same as -x=y). In all these cases |x| = |y| holds true. Therefore In |x|=|y| must be true as x=+-y.
III. \(\frac{x^2}{y^2}=1\). =>\(x^2=y^2\)
Answer is D. II and III only
Please hit +1 Kudos if you liked the answer.
23 May 2019, 22:41
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Bunuel
If \(x^2 - y^2 = 0\) and \(xy \neq 0\), which of the following MUST be true?
I. x = y
II. |x| = |y|
III. \(\frac{x^2}{y^2}=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
I. x = y
II. |x| = |y|
III. \(\frac{x^2}{y^2}=1\)
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
We can say that X*Y not= 0 and x= either y or (-y), we don't know for sure.
I. x = y, maybe true, may not iff x= (-y)
II. |x| = |y|, always true even if either of them is true: x=y or x=-y
III. \(\frac{x^2}{y^2}=1\), both numerator and denominator when squared will give the same value. (x=+/-y)
II and III must be true. D
