If \(XY ≠ 0\) and \(X^3Y = XY^3\), then which of the following must be true?

I) \(|X| = -|Y|\)
II) \(|X| = |Y|\)
III) \(X = Y = 1\)

A) None
B) II only
C) III only
D) I and II only
E) I, II, and III
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If XY≠0XY≠0 and X3Y=XY3X3Y=XY3, then which of the following must be true?

I) |X|=−|Y||X|=−|Y|
II) |X|=|Y||X|=|Y|
III) X=Y=1X=Y=1

A) None
B) II only
C) III only
D) I and II only
E) I, II, and III

IMO B
1- |X| = -|Y|
Not sufficient coz modulus never gives a negative value ,

2- |X| = |Y|
4 cases but it will always end up in 2 saying x=Y or x= -Y
Upon simplifying the original equation we will get
Xy= 0 - not possible
X= Y or x= -y
Sufficient

3- x=Y=1
Not sufficient coz x and u could 2 and 2 or 3 and 3 or 2 and -2
Not sufficient

So answer is B

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KanishkM

If C must be true ie X=Y=1 that means X & Y cant hold any other value, other than 1.

However, X=Y=2 or X=Y=3 also achieves the condition mentioned in the question.