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

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Question Stats: 49% (01:15) correct 51% (01:16) wrong based on 240 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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Manager  Joined: 21 Feb 2012
Posts: 56
Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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1
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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Intern  Joined: 26 May 2014
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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2
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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1
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).
Intern  Joined: 16 Dec 2014
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Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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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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2
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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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2
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

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

Co-Founder & GMAT Assassin Follow
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: 14 Location: United States Concentration: Sustainability, Sustainability Re: If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 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: 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: 56 Re: If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 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 D Joined: 04 Jan 2015 Posts: 2709 If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 1 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 _________________  Register for free sessions Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760 Success Stories Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories Ace GMAT Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA Must Read Articles Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2 Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2 Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry Algebra- Wavy line | Inequalities Practice Questions Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13755 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If y is a nonzero integer, what is the value of |y|? [#permalink] ### Show Tags 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 Follow Special Offer: Save$75 + GMAT Club Tests Free
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GMAT 1: 750 Q50 V41 Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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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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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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GMAT 1: 750 Q50 V41 Re: If y is a nonzero integer, what is the value of |y|?  [#permalink]

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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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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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