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# If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x

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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
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A.

(1) If $$y > 0$$, then $$x = 1$$ [ positive number divided by its absolute value is 1 ]
If $$y < 0$$, then $$x = -1$$ [ negative number divided by its absolute value is -1 ]
In both cases, value of $$x$$ is either 1 or -1, so $$|x| = 1$$. SUFFICIENT.

(2) $$|x| = -x$$
This is true for all x less than or equal to 0. NOT SUFFICIENT.
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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
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Bunuel wrote:
If $$y ≠ 0$$, is $$|x| = 1$$ ?

(1) $$x = \frac{y}{|y|}$$

(2) $$|x| = -x$$

NEW question from GMAT® Quantitative Review 2019

(DS05986)

From statement 1) x |y| = y

the only possible way for both sides to be equal if x = 0 or 1 or -1, however y cannot be zero.

so x is 1 or -1, sufficient.

From statement 2) |x| = -x

x can be 0 or -1

Insufficient.

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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
Salsanousi wrote:
Bunuel wrote:
If $$y ≠ 0$$, is $$|x| = 1$$ ?

(1) $$x = \frac{y}{|y|}$$

(2) $$|x| = -x$$

NEW question from GMAT® Quantitative Review 2019

(DS05986)

From statement 1) x |y| = y

the only possible way for both sides to be equal if x = 0 or 1 or -1, however y cannot be zero.

so x is 1 or -1, sufficient.

From statement 2) |x| = -x

x can be 0 or -1

Insufficient.

For statement 2, x could be negative anything or zero. x = -5, -x=5, |x| = 5
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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
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Bunuel wrote:
If $$y ≠ 0$$, is $$|x| = 1$$ ?

(1) $$x = \frac{y}{|y|}$$

(2) $$|x| = -x$$

$$|x|$$ means $$x$$ will take positive value only.

(1) $$x=1, \ if \ y>0, \ x=-1 \ if \ y<0,$$ but ultimately $$x=1 \ as \ x=|x|$$; Sufficient.

(2) It could be numerous values less than 0. Insufficient.

The answer is $$A$$
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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
If y≠0, is |x|=1?

(1) x=y/|y|
y = 1 YES
y = -1 YES
y = 2 YES
y = -2 YES

ad infinitum for any real integer.

Sufficient.

(2) |x|=−x
x = -1 YES
x = 0 NO
Insufficient.

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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
Hi,

Can someone please explain what does the sign |...| means? (e.g |x|)

Thank you !
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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]

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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
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Re: If y 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink]
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