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If x^4 + y^4 = 100, then the greatest possible value of x

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If x^4 + y^4 = 100, then the greatest possible value of x [#permalink] New post 07 Aug 2010, 08:25
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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.
[Reveal] Spoiler: OA
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Re: x^4+y^4, GMATprep [#permalink] New post 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).

Answer: B.
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Re: x^4+y^4, GMATprep [#permalink] New post 07 Aug 2010, 08:46
Yep, very easy, missed that y could be zero.
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Re: x^4+y^4, GMATprep [#permalink] New post 07 Aug 2010, 08:48
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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Re: algebra problem from practice test 1 GMAT software [#permalink] New post 28 Oct 2010, 18:35
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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.
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Re: x^4+y^4, GMATprep [#permalink] New post 25 May 2011, 05:57
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] New post 10 Apr 2012, 08:35
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

:wink:
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Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink] New post 03 Jul 2013, 00:24
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If x^4 + y^4 = 100, then the greatest possible value of x   [#permalink] 03 Jul 2013, 00:24
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