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

Question

(1) y^x = y

(2) x > 1

chetan2u · Answer

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
eq{0} 
Insuff

(2) x > 1
Nothing about y..
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

TRINA6 · Answer

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!

fskilnik · Answer

x,y\,\,{	ext{ints}}

? = y

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

The correct answer is therefore (E).

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

Regards, 
Fabio.

chetan2u · Answer

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

fskilnik · Answer

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.

chetan2u · Answer

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

TRINA6 · Answer

Make sense and much clear to me now. Thank you for the explanation

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?

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