Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:22

### 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 integers, what is the value of y?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Nov 2018
Posts: 19
Location: India
If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

Updated on: 27 Dec 2018, 12:59
2
3
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:43) correct 41% (01:37) wrong based on 91 sessions

### HideShow timer Statistics

If x and y are integers, what is the value of y?

(1) y^x=1

(2) (16 - 2x)/x = -x - 10

Originally posted by divyadamahe on 27 Dec 2018, 06:27.
Last edited by Bunuel on 27 Dec 2018, 12:59, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 08 Sep 2008
Posts: 136
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE: Operations (Transportation)
Re: If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

27 Dec 2018, 07:14
1
1
St:1
Y to power x =1
Y can be any integer if x is zero. So Not sufficient.
St:2
(16-2x)/x = -x-10
Solving
We get x=-4
No answer for Y. Not sufficient.

Combine:
X=-4 then only value of y is 1.
Sufficient.
_________________
Regards;
Vishal

+==========+
Kudos if it deserve....one...
Intern
Joined: 18 Dec 2017
Posts: 1
Re: If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

27 Dec 2018, 13:36
1
vishalkazone wrote:
St:1
Y to power x =1
Y can be any integer if x is zero. So Not sufficient.
St:2
(16-2x)/x = -x-10
Solving
We get x=-4
No answer for Y. Not sufficient.

Combine:
X=-4 then only value of y is 1.
Sufficient.

What about y=-1?. Even if we combine both statements, we can still get 2 values of y, that being 1 and -1.
General GMAT Forum Moderator
Joined: 15 Jan 2018
Posts: 435
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
Re: If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

28 Dec 2018, 10:13
Solution:

Given that, x and y are integers. We are asked to find the value of y.

Statement 1: y^x=1
For x=0, y can take any integer value.
Integer Property: Any number (except zero) raised to power zero is one; zero raised to power zero is undefined.
So, y can be any number.
For instance, 2^0=1, (-2)^0=1, 4^0=1
Since we do not get an unique value of y from Statement 1, this statement is NOT sufficient.

Statement 2: (16 - 2x)/x = -x - 10
x^2 + 8x + 16 = 0
(x + 4)^2 = 0
Solving the quadratic equation, we get two equal root of x, i.e. x = -4, -4
From Statement 2, we can only know the value of x, but not y. So, Statement 2 by itself NOT sufficient.

Combining Statement 1 & Statement 2
y^x=1 and x = -4
y^(-4)=1
Therefore, y^4 = 1
Two value of y satisfies the above equation, i.e. y = 1 & y = -1
Since we do not get an unique value of y even after combining Statement 1 & Statement 2, these statements are together NOT sufficient.

Hence, the correct answer is Option E.

_________________
New to GMAT Club or overwhelmed with so many resources? Follow the GMAT Club Study Plan!
Not happy with your GMAT score? Retaking GMAT Strategies!

Game of Timers - Join the Competition to Win Prizes
VP
Joined: 09 Mar 2018
Posts: 1002
Location: India
Re: If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

01 Feb 2019, 23:33
If x and y are integers, what is the value of y?

(1) y^x=1

(2) (16 - 2x)/x = -x - 10

x and y are integers, they can be +ive or -ive

from 1, y can be either -1 or 1

(-1)^0 = 1 or (1)^0 = 1

from 2, when we solve the quadratic equation
16 - 2x = -x^2 - 10x
x^2 - 8x + 16= 0
We get value of x as -4

when we combine both the statements the equation(1) becomes

y^-4 = 1
1/y^4 = 1

Now y can be either 1 or -1

which makes the answer as E

Thank you for your help on this.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Manager
Joined: 01 Nov 2018
Posts: 75
GMAT 1: 690 Q48 V35
GPA: 3.88
Re: If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

02 Feb 2019, 06:48
The correct answer should be E as combining both statements, we get 1/y^4=1 Cross multiply to get y^4=1 and y could be +/- 1.
Intern
Joined: 21 Jan 2019
Posts: 7
Re: If x and y are integers, what is the value of y?  [#permalink]

### Show Tags

02 Feb 2019, 07:08
X= -4...
Combining both statement... We get y^-4 = 1
This is nothing but 1/y^4 = 1...
Since 4 is an even integer... We get two possible solutions for y being 1 and-1... And both of the numbers will yield 1 as a result.... Therefore both statements combined is not sufficient to answer the question. Option E is the right choice.

Posted from my mobile device
Re: If x and y are integers, what is the value of y?   [#permalink] 02 Feb 2019, 07:08
Display posts from previous: Sort by