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17 Jul 2016, 10:36
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D
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Difficulty:
25%
(medium)
Question Stats:
72% (00:58) correct
28%
(01:02)
wrong
based on 4426
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If \(\frac{x}{|y|} = -1\) which of the following must be true?
(A) \(x = -y\)
(B) \(x = y\)
(C) \(x = y^2\)
(D) \(x^2 = y^2\)
(E) \(x^3 = y^3\)
(A) \(x = -y\)
(B) \(x = y\)
(C) \(x = y^2\)
(D) \(x^2 = y^2\)
(E) \(x^3 = y^3\)
17 Jul 2016, 10:43
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If \(\frac{x}{|y|} = -1\) which of the following must be true?
(A) \(x = -y\)
(B) \(x = y\)
(C) \(x = y^2\)
(D) \(x^2 = y^2\)
(E) \(x^3 = y^3\)
Given: \(\frac{x}{|y|} = -1\);
Cross-multiply: \(|y| = -x\), this implies that x is 0 or negative.
Square: \(y^2 = x^2\).
Answer: D.
Alternatively you can try number plugging: try x = -2 and y = 2 or -2. You'll see that only D is always true.
(A) \(x = -y\)
(B) \(x = y\)
(C) \(x = y^2\)
(D) \(x^2 = y^2\)
(E) \(x^3 = y^3\)
Given: \(\frac{x}{|y|} = -1\);
Cross-multiply: \(|y| = -x\), this implies that x is 0 or negative.
Square: \(y^2 = x^2\).
Answer: D.
Alternatively you can try number plugging: try x = -2 and y = 2 or -2. You'll see that only D is always true.
17 Jul 2016, 10:56
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Avigano
Hi! There,
x/|y| = -1
x= -1 |y|
Squaring both sides
x^2= (-1 |y|) ^2= y^2
D is the answer
Squaring any -ve number yields +ve number.
Let's see why other options are not right
A) x = -y What if x= 2 and y= 2. This does'nt hold good then.
B) x = y If x=-2 and y=2. This is not right.
C) x = y^2 This means x is +ve and |y| is always +ve. In this case x/|y| can not be -ve. not correct.
D) x^2 = y^2. Explained above.
E) x^3 = y^3. If x= -2 and y= 2. This will not hold true.
D is the answer
