Arithmetic + Algebra Arithmetic Operations + Inequalities

If x and y are nonzero integers, is x^y < y^x ?

1) x = y^2

2) y > 2

Stm I

y=1 x=1

1^1 = 1^1

x^y = y^x

y=3 x=9

x^y < y^x

INSUFF

Stmt II
y>2

No idea about x so INSUFF

Together

x = y^2
y>2

x^y = (y^2)^y = y ^2y

For y>2, 2y < y^2

So x^y i.e (y^2y) < y^x


Choose C

Hope this helps!

Regards,
CR

cramya wrote:
For y>2, 2y < y^2

So x^y i.e (y^2y) < y^x
CR

Can you please help me by explaining more on how you got the 2y and y^2? I just want to make sure so that I'm not assuming anything

P.S. Since x^y = (y^2)^y = y ^2y. Can we switch the y and ^2y to determine y^x ? Which would be (2y)^y? That would still lead us to the same conclusion???

Thank you, Cramya!

Can you please help me by explaining more on how you got the 2y and y^2? I just want to make sure so that I'm not assuming anything

Using exponent rule:

(a^b)^c = a^(b*c)

<=> (y^2)^y = y ^ (2*y) i.e y ^ (2y)

In the prob above a = y b=2 c=y Hence (y^2)^y became y ^ 2y

Can we switch the y and ^2y to determine y^x

No since y is not equal to 2y. Please see exponent rule explanation above.


Regards,
CR

Cramya I am thinking of contacting GMAC to hire you to design DS problems I am sure nobody on earth has more experience than you do.

logitech wrote:Cramya I am thinking of contacting GMAC to hire you to design DS problems I am sure nobody on earth has more experience than you do.

And I'll go contact the guinness book of world record people meanwhile. I think he has a world record in solving DS question

Thanks Guys/Gals or should I just say my good friends Logi/Mals.Much appreciated so do put in a word

I have no doubts that Logitech has a few contacts with his 2 minutes to an MBA quotes which I just love with a passion....

Regards,
Cramya

It makes a lot more sense now! Thank you, Cramya... you are indeed well-versed in DS. I am sure that GMAC can definitely use someone like you

But remember Cramya is on our side now, and GMAC can use his power against us! That would be scary!

Hats off to you master, I can't wait to see you give GMAT a good beat!!