GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 06:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If x and y are negative integers such that x = x^y + y, what is x?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47037
If x and y are negative integers such that x = x^y + y, what is x? [#permalink]

### Show Tags

25 Sep 2017, 23:35
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:19) correct 38% (01:46) wrong based on 52 sessions

### HideShow timer Statistics

If x and y are negative integers such that x = x^y + y, what is x?

(1) x – x^y = –2
(2) y = –2

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
If x and y are negative integers such that x = x^y + y, what is x? [#permalink]

### Show Tags

26 Sep 2017, 02:44
1
Bunuel wrote:
If x and y are negative integers such that x = x^y + y, what is x?

(1) x – x^y = –2
(2) y = –2

$$x = x^y + y$$ or $$x-x^y = y$$

Statement 1: this implies that $$y = -2$$. putting the value of $$y$$ in question stem equation we get

$$x-x^{-2}=-2$$

$$x-\frac{1}{x^2} = -2$$, as $$x$$ is a negative integer, only $$x=-1$$ satisfies this equation. Hence sufficient

Statement 2: Directly provides the value of $$y$$. As explained above only $$x=-1$$ satisfies the equation. Hence sufficient

Option D

---------------------------------------------------

Factorization to find the value of $$x$$

$$x-\frac{1}{x^2} = -2$$ or $$x^3+2x^2-1=0$$

here $$f(x)=x^3+2x^2-1$$, Notice that $$f(-1)=0$$, or $$x=-1$$ is a root of the equation, so $$x+1=0$$ is a factor of the equation.

Divide the equation by $$(x+1)$$ to get $$x^3+2x^2-1=(x+1)(x^2+x-1) =0$$,

Now $$x$$ is a negative integer, so for any value of $$x$$, $$x^2+x-1$$ will not be $$0$$

Hence $$x+1=0$$ or $$x=-1$$
Director
Joined: 21 Mar 2016
Posts: 537
Re: If x and y are negative integers such that x = x^y + y, what is x? [#permalink]

### Show Tags

26 Sep 2017, 10:56
niks18 wrote:
Bunuel wrote:
If x and y are negative integers such that x = x^y + y, what is x?

(1) x – x^y = –2
(2) y = –2

$$x = x^y + y$$ or $$x-x^y = y$$

Statement 1: this implies that $$y = -2$$. putting the value of $$y$$ in question stem equation we get

$$x-x^{-2}=-2$$

$$x-\frac{1}{x^2} = -2$$, as $$x$$ is a negative integer, only $$x=-1$$ satisfies this equation. Hence sufficient

Statement 2: Directly provides the value of $$y$$. As explained above only $$x=-1$$ satisfies the equation. Hence sufficient

Option D

---------------------------------------------------

Factorization to find the value of $$x$$

$$x-\frac{1}{x^2} = -2$$ or $$x^3+2x^2-1=0$$

here $$f(x)=x^3+2x^2-1$$, Notice that $$f(-1)=0$$, or $$x=-1$$ is a root of the equation, so $$x+1=0$$ is a factor of the equation.

Divide the equation by $$(x+1)$$ to get $$x^3+2x^2-1=(x+1)(x^2+x-1) =0$$,

Now $$x$$ is a negative integer, so for any value of $$x$$, $$x^2+x-1$$ will not be $$0$$

Hence $$x+1=0$$ or $$x=-1$$

any easier way to solve this????
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
Re: If x and y are negative integers such that x = x^y + y, what is x? [#permalink]

### Show Tags

26 Sep 2017, 11:01
Quote:
any easier way to solve this????

Hi mohshu

I find this to be a very simple process as both the statements directly provide the value of y.
and since x is negative only one value of x satisfies the given equation.

Is there any specific question that i can address? and if you are finding the factorization process confusing, then that is just an FYI
Re: If x and y are negative integers such that x = x^y + y, what is x?   [#permalink] 26 Sep 2017, 11:01
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.