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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).

\(x^4 + y^4 = 100\) 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: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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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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08 Aug 2015, 12:50

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Dear Bunuel. i learnt that x square is IxI = + or - or absolute value of X. right ? if right so why here we assume that X = +ve 3.2 ?

That is because of the options provided are positive ranges. You dont want to spend time on irrelevant things such as the negative values.
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19 Jan 2017, 07:43

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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19 Jan 2017, 15:18

This was my approach. Since it doesn't state that X & Y are integers, I can assume that the answer could very well fall between integers. So, since we're looking for the max of X, I will just assume Y^4 is just 0^4.

Therefore, if X = 3, then 3^4 = 81. If X = 4, then 4^4 = 256.

So X is between 3 and 4. The answer that falls under that qualification is B.

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

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15 Feb 2017, 05:08

The key to solving this problem for me was understanding that x is the maximum, when y is the minimum. Since y is raised to the fourth power, the smallest y can be is 0.

Here is the full solution: \(x^4+y^4=100\) \(x^4+0=100\) \(x^4=100\) \(x^2=10\) \(x=\sqrt{10}\) \(4>x>3\)

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