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If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]
 07 Aug 2010, 09:25
Question Stats:
51% (01:50) correct
48% (00:45) wrong based on 3 sessions
If x^4 + y^4 = 100, then 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 How (B) could be an answer? Consider x=5.5, then x^4 is already bigger than 100. And y^4 can't be -ve.
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Re: x^4+y^4, GMATprep [#permalink]
07 Aug 2010, 09:40
ulm wrote: Please find the attached pict.
How (B) could be an answer?
Consider x=5.5, then x^4 is already bigger than 100. And y^4 can't be -ve. If x^4+y^4=100, then the greatest possible value of x is betweenA. 0 and 3 B. 3 and 6 C. 6 and 9 D. 9 and 12 E. 12 and 15 General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.So, to maximize x we should minimize y^4. Least value of y^4 is zero. In this case x^4+0=100 --> x^4=100 --> x^2=10 --> x=\sqrt{10}\approx{3.2}, which is in the range (3,6). Answer: B.
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Re: x^4+y^4, GMATprep [#permalink]
07 Aug 2010, 09:46
Yep, very easy, missed that y could be zero.
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Re: x^4+y^4, GMATprep [#permalink]
07 Aug 2010, 09:48
My attempt: If x^4+y^4=100, then the greatest possible value of x would be when y is minimum. Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B Hence answer is -- b) 3 and 6.
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Greatest possible value of x [#permalink]
05 Sep 2010, 11:32
If x^4 + y^4 = 100, then the greatest possible value of x is between
1) 0 and 3
2) 3 and 6
3) 6 and 9
4) 9 and 12
5) 12 and 15
I chose 1. However, OA is different.
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Re: Greatest possible value of x [#permalink]
05 Sep 2010, 12:41
Bunuel wrote: Merging similar topics. Thanks. Did a small mistake of only assuming integer value of x and thus chose A. Many thanks.
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Re: algebra problem from practice test 1 GMAT software [#permalink]
28 Oct 2010, 19:35
x^4 + y^4 = 100When you see even powers, first thing that should come to your mind is that the term will be positive or zero. If you want to maximize x in the sum, you should minimize y^4 so that this term's contribution in 100 is minimum possible. Since it is an even power, its smallest value is 0 when y = 0. Then x^4 = 100 Since 3^4 = 81 and 4^4 = 256,x will lie between 3 and 4.
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Re: x^4+y^4, GMATprep [#permalink]
25 May 2011, 06:57
Step 1:
x^4+y^4=100
x^4 will be maximum when y^4 is minimum. Lets assume y=0.1 so, y^4=0.0001
Step 2:
x^4+1^4=100
=> x^4+0.0001=100
=>x^4=100-0.0001
=>x^4=99.9999
Lets substitute x=3, i.e 3*3*3*3 = 81
So the value of x can be little more than 3 because 4*4*4*4=256
So the answer is option (B)
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Re: x^4+y^4, GMATprep [#permalink]
10 Apr 2012, 09:35
Two things that we must consider in order to solve this problem are: a) We do not look for an integer b) We do not look for a specific number but we want to see the number we are looking for in what range falls....e.x it is positive ot it is greater than 10.....in our example all the answers give range.... solution has been given by minimizing Y meaning Y=0 
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Re: x^4+y^4, GMATprep
[#permalink]
10 Apr 2012, 09:35
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