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

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If x and y are integers, what is the value of y?  [#permalink]

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New post Updated on: 27 Dec 2018, 12:59
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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.
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Re: If x and y are integers, what is the value of y?  [#permalink]

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New post 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.
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Re: If x and y are integers, what is the value of y?  [#permalink]

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New post 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.
Please let me know your thoughts.
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Re: If x and y are integers, what is the value of y?  [#permalink]

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New post 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.

divyadamahe - Could you please review the OA?
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Re: If x and y are integers, what is the value of y?  [#permalink]

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

(1) y^x=1

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


IMO answer should be E

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

divyadamahe can you please confirm on the OA once??

Thank you for your help on this.
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Re: If x and y are integers, what is the value of y?  [#permalink]

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New post 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.
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Re: If x and y are integers, what is the value of y?  [#permalink]

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New post 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.

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Re: If x and y are integers, what is the value of y?   [#permalink] 02 Feb 2019, 07:08
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