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

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

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New post 23 Aug 2008, 03:22
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-4-y-4-100-then-the-greatest-possible-value-of-x-is-128171.html
[Reveal] Spoiler: OA

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kris


Last edited by Bunuel on 19 Jul 2013, 01:54, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: Greatest Possible values of x? [#permalink]

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New post 23 Aug 2008, 03:41
krishan wrote:
If x4 + y4 = 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

x4 is x raised to the power of 4 (I could not figure out how to show it as an exponent)

Thanks


Greatest possible value of X when Y^4 is minimum.
The possible minimum value of Y^4 is 0
\(X^4=100 ---> X^2=10
--> X> 3 AND X<4\)
B is the answer.
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Re: Greatest Possible values of x? [#permalink]

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New post 23 Aug 2008, 04:32
Thanks a lot Suresh.
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Re: Greatest Possible values of x? [#permalink]

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New post 23 Aug 2008, 23:09
shailyam,
The ans should be B not A since values geater than 3 also satify the equation e.g. x = 3.1 can also be possible.
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Re: Greatest Possible values of x? [#permalink]

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New post 19 Jul 2013, 01:00
LoyalWater wrote:
shailyam,
The ans should be B not A since values geater than 3 also satify the equation e.g. x = 3.1 can also be possible.



Going by your logic, one can consider 3.1 as a possible value of x. Here we're not sure of the value of x and saying that the greatest possible value of x is between 3 and 6 would mean that x could be even more than 3.1, for example 4. Hence, answer is A
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Re: Greatest Possible values of x? [#permalink]

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New post 19 Jul 2013, 01:54
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kshitij90 wrote:
LoyalWater wrote:
shailyam,
The ans should be B not A since values geater than 3 also satify the equation e.g. x = 3.1 can also be possible.



Going by your logic, one can consider 3.1 as a possible value of x. Here we're not sure of the value of x and saying that the greatest possible value of x is between 3 and 6 would mean that x could be even more than 3.1, for example 4. Hence, answer is A


That's not correct.

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.

Hope it's clear.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-4-y-4-100-then-the-greatest-possible-value-of-x-is-128171.html
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Re: Greatest Possible values of x?   [#permalink] 19 Jul 2013, 01:54
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