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If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x
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Bunuel
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If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  03 Aug 2018, 04:26
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If \(y ≠ 0\), is \(|x| = 1\) ?


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

(2) \(|x| = -x\)


NEW question from GMAT® Quantitative Review 2019


(DS05986)
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PKN
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  03 Aug 2018, 04:44
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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)


Question stem, is \(|x| = 1\) ?

St1:- \(x = \frac{y}{|y|}\)
When y>0, \(x = \frac{y}{y}\) (where y is non-negative and non-zero)
Or, x=1; so |x|=1

when y<0, \(x = \frac{y}{-y}\)
Or, x=-1; so |x|=1
Sufficient.

St2:- \(|x| = -x\)
Or, \(|x|+x=0\)
Or, \(x\leq0\)
Insufficient.

Ans. (A)
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  03 Aug 2018, 04:42
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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] New post  19 Oct 2018, 08:57
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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

Two different answers.

Insufficient.

Answer choice A
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  04 Mar 2020, 19:47
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

Two different answers.

Insufficient.

Answer choice A


For statement 2, x could be negative anything or zero. x = -5, -x=5, |x| = 5
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If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  27 Dec 2020, 13:14
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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] New post  25 Jan 2021, 20:47
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.

Answer is A.
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Dana2708
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  01 Apr 2021, 09:00
Hi,

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

Thank you !
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Bunuel
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x [#permalink] New post  01 Apr 2021, 10:06
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Dana2708 wrote:
Hi,

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

Thank you !


|x| denotes the absolute value or modulus of a real number x.

10. Absolute Value



For more check Ultimate GMAT Quantitative Megathread



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