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Re: x^4+y^4, GMATprep [#permalink]
07 Aug 2010, 08:40

Expert's post

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 between A. 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).

Re: algebra problem from practice test 1 GMAT software [#permalink]
28 Oct 2010, 18:35

2

This post received KUDOS

Expert's post

x^4 + y^4 = 100 When 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. _________________

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