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

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Math Expert
Joined: 02 Sep 2009
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If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 04:26
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55% (hard)

Question Stats:

48% (00:54) correct 52% (00:52) wrong based on 65 sessions

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

(1) y^x = y

(2) x > 1

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7097
If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 08:05
If x and y are integers, what is the value of y?

(1) y^x = y
$$y^x-y=0......y(y^{x-1}-1)=0$$
So either y=0 or $$y^{x-1}=1$$, that is x is 1 or y is 1 if $$x\neq{0}$$
Insuff

(2) x > 1
Insufficient

Combined
Either y=0, or y=1,
And when x is odd, y can be 0, 1 or -1 for example y^3=y....y^3-y=0...y(y-1)(y+1)=0
Insufficient

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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

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26 Sep 2018, 09:09
Bunuel wrote:
If x and y are integers, what is the value of y?

(1) y^x = y

(2) x > 1

St2: alone is not sufficient but it gives information about X; X is positive and more than 1

Now coming back to St1: y^x = y This is only possible when y=1

No matter what is the value of X (eg. 2,3,4,5..100), y^x = y will always hold true.

My ans is C; please correct me if I am missing something!
GMATH Teacher
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Re: If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 13:48
Bunuel wrote:
If x and y are integers, what is the value of y?

(1) y^x = y

(2) x > 1

$$x,y\,\,{\text{ints}}$$

$$? = y$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {x,y} \right) = \left( {2,0} \right)\,\,\,\, \Rightarrow \,\,\,? = 0\,\, \hfill \\ \,{\text{Take}}\,\,\left( {x,y} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,{\text{?}}\,{\text{ = }}\,{\text{1}}\,\, \hfill \\ \end{gathered} \right.$$

The correct answer is therefore (E).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Joined: 02 Aug 2009
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If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 19:07
TRINA6 wrote:
Bunuel wrote:
If x and y are integers, what is the value of y?

(1) y^x = y

(2) x > 1

St2: alone is not sufficient but it gives information about X; X is positive and more than 1

Now coming back to St1: y^x = y This is only possible when y=1

No matter what is the value of X (eg. 2,3,4,5..100), y^x = y will always hold true.

My ans is C; please correct me if I am missing something!

Yes you are missing something....
What if x is even y^2=y, here y can be 1 or 0
And when x is odd, say 3..y^3=y... Here y can be 0, 1 or -1
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 534
Re: If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 19:15
1
chetan2u wrote:
Yes you are missing something....
What if x is even y^2=y, here y can be 1 or -1

Hi, chetan2u!
Just to correct your typo: when y^x = y and x=2, you mean y can be 1 or 0 (not -1), of course.
Regards,
Fabio.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Math Expert
Joined: 02 Aug 2009
Posts: 7097
Re: If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 19:20
1
fskilnik wrote:
chetan2u wrote:
Yes you are missing something....
What if x is even y^2=y, here y can be 1 or -1

Hi, chetan2u!
Just to correct your typo: when y^x = y and x=2, you mean y can be 1 or 0 (not -1), of course.
Regards,
Fabio.

Thank you Fabio..
Of course y cannot be negative ..
It was a typo and I meant odd value of X..
Example (-1)^3=-1 so y can be -1 too
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 10 Jul 2017
Posts: 10
Re: If x and y are integers, what is the value of y?  [#permalink]

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26 Sep 2018, 21:54
chetan2u wrote:
TRINA6 wrote:
Bunuel wrote:
If x and y are integers, what is the value of y?

(1) y^x = y

(2) x > 1

St2: alone is not sufficient but it gives information about X; X is positive and more than 1

Now coming back to St1: y^x = y This is only possible when y=1

No matter what is the value of X (eg. 2,3,4,5..100), y^x = y will always hold true.

My ans is C; please correct me if I am missing something!

Yes you are missing something....
What if x is even y^2=y, here y can be 1 or 0
And when x is odd, say 3..y^3=y... Here y can be 0, 1 or -1

Make sense and much clear to me now. Thank you for the explanation
Re: If x and y are integers, what is the value of y? &nbs [#permalink] 26 Sep 2018, 21:54
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