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Bunuel
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If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0 04 Jan 2024, 02:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

67% (01:21) correct 33% (01:20) wrong based on 119 sessions

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If \(xy=y\), what is the value of \(|x|+|y|\)?

(1) \(x=-1\)
(2) \(y=0\)

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A
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cdrectenwald
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If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0 04 Jan 2024, 06:16
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I like A

When we know that X = -1 we then know that -y = y which I only believe is true for 0. This we know abs(x) + abs(y)

B is not sufficient because we don’t know x

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littlesourris
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If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0 01 Feb 2024, 01:37
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Does someone have the OA for this question ?
Why not B ?
xy=y => x= y/y=1 => |x| + |y| = 1+|y|
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Bunuel
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If xy = y, what is the value of |x| + |y|? (1) x = -1 (2) y = 0 01 Feb 2024, 02:54
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littlesourris
If \(xy=y\), what is the value of \(|x|+|y|\)?

(1) \(x=-1\)
(2) \(y=0\)

Does someone have the OA for this question ?
Why not B ?
xy=y => x= y/y=1 => |x| + |y| = 1+|y|
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You cannot reduce \(xy=y\) by y to get \(x=1\). That's because y can be 0, and we cannot divide by 0. By doing so, you lose a solution, namely y = 0.

What you can do is rearrange and factor out y:

    \(xy=y\)
    \(xy-y=0\)
    \(y(x-1)=0\)
    \(y=0\) or \(x=1\) (or both)

Never reduce an equation by a variable (or expression with a variable) if you are not certain that the variable (or expression containing the variable) is not equal to zero. We cannot divide by zero.

Back to the question;

If \(xy=y\), what is the value of \(|x|+|y|\)?

(1) \(x=-1\)

Since x = -1, then x is not 1, and thus y must be 0 for the equation (\(xy=y\)) to hold. Therefore, \(|x|+|y|=1+0=1\). Sufficient.

(2) \(y=0\)

When \(y=0\), then from \(xy=y\), x can be any number, therefore we cannot determine the specific value of \(|x|+|y|\). Not sufficient.

Answer: A.

Hope it's clear.
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