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# M31-48

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Math Expert
Joined: 02 Sep 2009
Posts: 54369

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20 Jun 2015, 12:04
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Difficulty:

55% (hard)

Question Stats:

55% (00:52) correct 45% (00:51) wrong based on 71 sessions

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If $$y$$ is a nonzero integer, what is the value of $$|y|$$?

(1) $$y^2 = |y|$$

(2) $$|y| = |y|!$$

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Math Expert
Joined: 02 Sep 2009
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20 Jun 2015, 12:04
Official Solution:

If $$y$$ is a nonzero integer, what is the value of $$|y|$$?

(1) $$y^2 = |y|$$

Since $$y^2 = |y|^2$$, then we have that $$|y|*|y| = |y|$$. $$y$$ is nonzero, so we can reduce by it: $$|y| = 1$$. Sufficient.

(2) $$|y| = |y|!$$

By testing values we can get that this holds true for $$y = +/-1$$ as well as for $$y = +/-2$$. Thus, $$|y| = 1$$ or 2. Not sufficient.

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06 May 2016, 15:41
Sorry I don't understand why solution 1 is correct, is there anything I need to review to get these kind of questions right? thank you
Math Expert
Joined: 02 Aug 2009
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06 May 2016, 19:35
1
Avigano wrote:
Sorry I don't understand why solution 1 is correct, is there anything I need to review to get these kind of questions right? thank you

y^2 = |y|..
which are the numbers which are equal to its squares.. 0, 1 and -1 here as we are taking |-1| here..
but we are told y is non-zero, so y =1 or -1.. in both cases the MOD |y| will be 1..
thus suff
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07 May 2016, 05:33
1
Avigano wrote:
Sorry I don't understand why solution 1 is correct, is there anything I need to review to get these kind of questions right? thank you

Theory on Absolute Values: math-absolute-value-modulus-86462.html
The E-GMAT Question Series on ABSOLUTE VALUE: the-e-gmat-question-series-on-absolute-value-198503.html
Properties of Absolute Values on the GMAT: properties-of-absolute-values-on-the-gmat-191317.html
Absolute Value: Tips and hints: absolute-value-tips-and-hints-175002.html

DS Absolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Absolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Absolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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Joined: 17 Aug 2015
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10 Dec 2016, 20:07
can some one please explain |y|! ?
Current Student
Joined: 12 Nov 2015
Posts: 59
Location: Uruguay
Concentration: General Management
Schools: Goizueta '19 (A)
GMAT 1: 610 Q41 V32
GMAT 2: 620 Q45 V31
GMAT 3: 640 Q46 V32
GPA: 3.97

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10 Dec 2016, 22:16
raul17 wrote:
can some one please explain |y|! ?

For this statement Y can have two values:
Y=1... 1!=1

Or

Y=2... 2!=2x1=2

So although the stem points out that Y is not zero, we are left with two possible values for Y (Y could be 1 or 2),

statment 2) alone is not sufficient,

kind regards.
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Joined: 08 Jun 2017
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13 Jul 2017, 16:34
I was looking at the value of y, not |y|.
Re: M31-48   [#permalink] 13 Jul 2017, 16:34
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