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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]

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07 Aug 2010, 08:25
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58% (00:54) correct 42% (01:01) wrong based on 814 sessions

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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

[Reveal] Spoiler:
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

Last edited by ENGRTOMBA2018 on 10 Jan 2016, 15:01, edited 1 time in total.
Formatted the question

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

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07 Aug 2010, 08:40
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ulm wrote:
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).

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

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07 Aug 2010, 08:46
Yep, very easy, missed that y could be zero.

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

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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

b) 3 and 6.
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Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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

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

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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

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

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03 Jul 2013, 00:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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08 Aug 2015, 11:50
Hello from the GMAT Club BumpBot!

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

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12 Sep 2015, 19:43
In my opinion, the question should specify that the x and y are integers. If y is 1/2, for instance, x could be within a different range.

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

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13 Sep 2015, 03:32
RudyBaylor wrote:
In my opinion, the question should specify that the x and y are integers. If y is 1/2, for instance, x could be within a different range.

Please re-read the question and the solutions provided. None of them is treating x and y as integers only.
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Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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10 Jan 2016, 14:52
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 ?

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

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10 Jan 2016, 15:23
hatemnag wrote:
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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Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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19 Jan 2017, 06:43
Hello from the GMAT Club BumpBot!

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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, 14:18
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.

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

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15 Feb 2017, 04:08
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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Re: If x^4 + y^4 = 100, then the greatest possible value of x [#permalink]

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16 Feb 2017, 11:14
ulm wrote:
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

In determining the greatest possible value of x, we want to minimize y^4. Since the minimum value of y^4 is 0 (when y = 0), we have:

x^4 + 0 = 100

x^4 = 100

x^2 = 10

x = +/-√10

x ≈ 3.2 or -3.2

Thus, we see that the greatest value of x is between 3 and 6.

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Re: If x^4 + y^4 = 100, then the greatest possible value of x   [#permalink] 16 Feb 2017, 11:14
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