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

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If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 05:33
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If y is a nonzero integer, what is the value of |y|?

(1) y^2 = |y|
(2) |y| = |y|!
[Reveal] Spoiler: OA

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Joined: 21 Feb 2012
Posts: 59
Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 06:47
1
KUDOS
Hello all

My attempt:

We need to find $$|y|$$ where $$y$$ is a non zero integer

Statement 1:

$$y^2 = |y|$$
$$y^2 - |y| = 0$$
Assume $$y$$ is $$+ve$$ then
$$y^2 - y = 0$$
Gives two solutions $$y = 0$$ and $$y = 1$$ we drop $$y = 0$$ as it is not valid. Therefore $$y = 1$$ is a solution for $$y>0$$
Now assume $$y$$ is $$-ve$$ then
$$y^2 + y = 0$$
This too gives two solutions $$y = 0$$ and $$y = -1$$ and again we drop $$y = 0$$. Therefore $$y = -1$$ is a solution for $$y<0$$
Overall two solutions are valid $$y = 1$$ and $$y = -1$$ and both have absolute values as $$y = 1$$
Hence solvable from this statement.

Statement 2:

$$|y| = |y|!$$
Lets assume for case $$y$$ is $$+ve$$
$$y = y!$$
$$y*[(y-1)! - 1] = 0$$
Here the solutions are $$y = 0$$, $$y = 1$$, $$y = 2$$ we drop $$y = 0$$ and hence leftover solutions are $$y = 1$$ and $$y = 2$$
Now if $$y$$ is $$-ve$$ then again we will be reducing the equation to the same expression.
Hence absolute value of $$y$$ can take $$1$$ or $$2$$.
Thus not solvable from this statement.

I will go with option $$A$$
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J

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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 07:55
2
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My Ans - A

Explanation :

(1) y^2 = |y|

This is true for only one value of y i.e. 1

Hence, this is sufficient to determine the value alone.

(2) |y| = |y|!

This is true for y=1 & y=2 . Hence, not sufficient to determine the value of |y|.
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 09:18
1
KUDOS
Quote:
If y is a nonzero integer, what is the value of |y|?

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

My Approach:

(1.) y^2 = |y|
Since, y is not zero. and is an integer, the only values of y which satisfy this are y=1 and y=-1. For both |y|=1.
So, Sufficient.

(2.)|y| = |y|!
Now, y can be -1,1,-1, or 2. And |y| can be 1 or 2.
So Insufficient.

Hence (A).
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Joined: 16 Dec 2014
Posts: 2
Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 10:13
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

I would say E, right? we are looking for the value of y and none of these gives us the true value… it could be 23422 or 2

I am new to this but none of the statements gives me the clue as to what the "value" of y is
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 10:31
2
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heylookitskarl wrote:
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

I would say E, right? we are looking for the value of y and none of these gives us the true value… it could be 23422 or 2

I am new to this but none of the statements gives me the clue as to what the "value" of y is

Note that we need to find value of |y| not y.
Now read both the points again.
Point (1) clearly gives a single value of |y| = 1.
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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29 May 2015, 11:29
2
KUDOS
Expert's post
Hi All,

This question is a great example of how sometimes you're NOT really being tested on high-level "math" skills - you're really being tested on the thoroughness of your thinking, your ability to see more than just the obvious answer and your attention to the question that is ASKED.

Here, we're told that Y is a NON-ZERO INTEGER. We're asked for the value of |Y|. It's worth remembering that the absolute value symbol turns negative results into positive ones....

Fact 1: Y^2 = |Y|

Since we're dealing with a squared term, there will likely be more than one solution to this equation (but not that many). As Y gets "more positive" or "more negative", the squared term will clearly become bigger than the |Y|, so the solution(s) must be fairly close to 0 (although remember that 0 is NOT allowed here).

IF....
Y = 1
1^2 = |1|
The answer to the question is |1| = 1

IF...
Y = -1
(-1)^2 = |-1|
The answer to the question is |-1| = 1
Fact 1 is SUFFICIENT

Fact 2: |Y| = |Y|!

Here, we're dealing with a factorial, so we also should be looking for relatively "small" answers (since a bigger Y would lead to a bigger Y!).

IF....
Y = 1
|1| = |1|!
The answer to the question is |1| = 1

IF....
Y = 2
|2| = |2|!
The answer to the question is |2| = 2
Fact 2 is INSUFFICIENT

[Reveal] Spoiler:
A

GMAT assassins aren't born, they're made,
Rich
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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 19 Mar 2015 Posts: 20 Location: United States Concentration: Sustainability, Sustainability Re: If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 30 May 2015, 01:48 EMPOWERgmatRichC wrote: Hi All, This question is a great example of how sometimes you're NOT really being tested on high-level "math" skills - you're really being tested on the thoroughness of your thinking, your ability to see more than just the obvious answer and your attention to the question that is ASKED. Here, we're told that Y is a NON-ZERO INTEGER. We're asked for the value of |Y|. It's worth remembering that the absolute value symbol turns negative results into positive ones.... Fact 1: Y^2 = |Y| Since we're dealing with a squared term, there will likely be more than one solution to this equation (but not that many). As Y gets "more positive" or "more negative", the squared term will clearly become bigger than the |Y|, so the solution(s) must be fairly close to 0 (although remember that 0 is NOT allowed here). IF.... Y = 1 1^2 = |1| The answer to the question is |1| = 1 IF... Y = -1 (-1)^2 = |-1| The answer to the question is |-1| = 1 Fact 1 is SUFFICIENT Fact 2: |Y| = |Y|! Here, we're dealing with a factorial, so we also should be looking for relatively "small" answers (since a bigger Y would lead to a bigger Y!). IF.... Y = 1 |1| = |1|! The answer to the question is |1| = 1 IF.... Y = 2 |2| = |2|! The answer to the question is |2| = 2 Fact 2 is INSUFFICIENT Final Answer: [Reveal] Spoiler: A GMAT assassins aren't born, they're made, Rich can you please reexplain why 2nd statement is not sufficient? Manager Joined: 21 Feb 2012 Posts: 59 Re: If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 30 May 2015, 01:56 Yogita25 wrote: can you please reexplain why 2nd statement is not sufficient? Hello Yogita25 Please note that the statement 2 is giving two values $$|y| = |y|!$$ Lets assume for case $$y$$ is $$+ve$$ $$y = y!$$ $$y*[(y-1)! - 1] = 0$$ Here the solutions are $$y = 0$$, $$y = 1$$, $$y = 2$$ we drop $$y = 0$$ and hence leftover solutions are $$y = 1$$ and $$y = 2$$ Now if $$y$$ is $$-ve$$ then again we will be reducing the equation to the same expression. Hence absolute value of $$y$$ can take $$1$$ or $$2$$. Thus not solvable from this statement. _________________ Regards J Do consider a Kudos if you find the post useful e-GMAT Representative Joined: 04 Jan 2015 Posts: 989 If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 30 May 2015, 02:00 1 This post received KUDOS Expert's post Yogita25 wrote: can you please reexplain why 2nd statement is not sufficient? Dear Yogita25 St. 2 says |y| = |y|! Now, the factorial of a positive integer n is defined as n(n-1)(n-2)(n-3) . . .1 For example, 4! = 4*3*2*1 Now, let |y| = n. So, as per St. 2, n = n! What can be the possible values of n? If n = 1, then n! = 1. So, n = n! If n = 2, then n! = 2*1 = 2. So, n = n! If n = 3, then n! = 3*2*1 = 6. So, n! > n For all values greater than 3 also, n! > n So, we see that the only possible values of n are: 1 and 2. That is, Either |y| = 1 Or, |y| = 2 So, from St. 2, we get two possible values of |y|. Since we could not find a unique value of |y|, St. 2 is not sufficient. I hope this helped clarify your doubt! Best Regards Japinder _________________ | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11486 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 30 May 2015, 12:14 Hi Yogita25, DS questions test you on a variety of skills - one of those skills is your ability to determine if an answer remains CONSISTENT or not. If, when including the information in Fact 1 or Fact 2, the answer to a given DS question CHANGES, then the data in the Fact is INSUFFICIENT to answer the question. In this DS question, I used the data in Fact 2 to prove that the answer CHANGES depending on the value of Y. Thus, Fact 2 is INSUFFICIENT. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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31 May 2015, 10:25
A
(1) y= -1 or +1; |y| = 1
(2) y = 1 or 2
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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01 Jun 2015, 04:10
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

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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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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01 Jun 2015, 05:02
apoorv601 wrote:
A
(1) y= -1 or +1; |y| = 1
(2) y = 1 or 2

For (2) y can also equal -1 and -2, my bad!!
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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24 Jul 2016, 06:52
Bunuel wrote:
If y is a nonzero integer, what is the value of |y|?

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

Statement 1. Since both parts are non-negative we can square both sides. Hence we have y^4 = y .Since y is not equal to zero we can divide both parts by y to get y^3 = 1 Hence y=1 Sufficient
Statement 2. Both 1 and 2 satisfy this condition. Hence not sufficient.
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Re: If y is a nonzero integer, what is the value of |y|? [#permalink]

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Re: If y is a nonzero integer, what is the value of |y|?   [#permalink] 13 Mar 2018, 04:53
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