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Arithmetic + Algebra Arithmetic Operations + Inequalities

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Source: — Data Sufficiency |
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by cramya » Tue Mar 10, 2009 9:45 pm
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
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by BlindVision » Wed Mar 11, 2009 9:52 am
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!
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by cramya » Wed Mar 11, 2009 2:12 pm
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.


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CR
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by logitech » Wed Mar 11, 2009 2:54 pm
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. B-)
LGTCH
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by mals24 » Wed Mar 11, 2009 2:58 pm
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. B-)
And I'll go contact the guinness book of world record people meanwhile. I think he has a world record in solving DS question :P
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by cramya » Wed Mar 11, 2009 3:14 pm
Thanks Guys/Gals or should I just say my good friends Logi/Mals.Much appreciated so do put in a word :D

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.... :P

Regards,
Cramya
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by BlindVision » Wed Mar 11, 2009 6:20 pm
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 :D
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by logitech » Thu Mar 12, 2009 8:52 pm
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!!
LGTCH
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