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GMAT PREP Exponents

by pkw209 » Tue Dec 29, 2009 10:32 am
Hey all,

Really baffled as to why the answer isn't B in this question. A brief explanation would be appreciated. Thanks!

70) If x4 + y4 = 100, the greatest possible value of x is between

a. 0 and 3
b. 3 and 6
c. 6 and 9
d. 9 and 12
e. 12 and 15
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by GMATowned » Tue Dec 29, 2009 10:49 am
Is the Question supposed to be

70) If x^4 + y^4 = 100, the greatest possible value of x is between

a. 0 and 3
b. 3 and 6
c. 6 and 9
d. 9 and 12
e. 12 and 15
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by aspirant1 » Tue Dec 29, 2009 4:25 pm
x^4 + y^4 = 100...i.e (x^2)^2 + (y^2)^2 = 10^2

x^2 + y^2 = 10

if x = 1, y = 3 can solve the equation

x = 1 is between 0 and 3

Ans: a

Any other ideas / methods !?
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by Stuart@KaplanGMAT » Tue Dec 29, 2009 7:05 pm
pkw209 wrote:Hey all,

Really baffled as to why the answer isn't B in this question. A brief explanation would be appreciated. Thanks!

70) If x^4 + y^4 = 100, the greatest possible value of x is between

a. 0 and 3
b. 3 and 6
c. 6 and 9
d. 9 and 12
e. 12 and 15
On most GMAT questions on which we're asked to maximize one thing, we want to minimize everything else. So, to maximize x, let's minimize y^4.

Since y^4 will never be negative, the smallest possible value for y^4 is 0. Therefore, to maximize x, we want to solve for:

x^4 + 0 = 100

or simply

x^4 = 100

Well, 3^4 is 81 and 4^4 is 256, so the greatest possible value of x is somewhere between 3 and 4: choose B.

If someone says the answer is anything else, they're wrong! What's the source?
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by Stuart@KaplanGMAT » Tue Dec 29, 2009 7:23 pm
aspirant1 wrote:x^4 + y^4 = 100...i.e (x^2)^2 + (y^2)^2 = 10^2

x^2 + y^2 = 10

if x = 1, y = 3 can solve the equation

x = 1 is between 0 and 3

Ans: a

Any other ideas / methods !?
Just FYI, this is really bad math.

The root of (x^4 + y^4) is NOT (x^2 + y^2). There's no simple root to that expression.
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by pkw209 » Wed Dec 30, 2009 11:54 am
Thanks guys. You all figured out that it's supposed to be exponents, sorry.

Yes, B is what I thought. I thought I was going crazy! Thanks Stuart!

Source was from Zuleron's 198 questions, which were all taken from GMAT PREP. However, I am starting to see that a few of the question stems and answers are not correct.
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by san2009 » Sun Jul 25, 2010 8:30 am
yeah be a bit cautious with zuleron. he's done a GREAT job of compiling them but naturally there are a few typos. if anyone has trouble with any specifics, pls feel free to msg me. I've navigated thru them in detail!
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