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If x and y are positive integers and x^4 + y^4 < 10,000, then the grea

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If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 24 May 2011, 06:55
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If x and y are positive integers and x^4 + y^4 < 10,000, 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

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 24 May 2011, 08:13
dreambeliever wrote:
If x and y are positive integers and x^4 + y^4< 10,000, 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


TO make X as big as possible, y^4 must be small. So if y = 1 then the equation is

x^4 + 1 < 10,000 or x^4 + 1 < 10 ^ 4

So you know x must be less than 10.

So option C is best answer.

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 24 May 2011, 22:20
I answered, D

x^4 + y^4 < 10,000
set y=1
x^4 < 9,999

10^4 = 10,000

so, x=9

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 25 May 2011, 06:29
Where is this from ? Looks like a modified version of this question.

x-4-y-4-gmatprep-98713.html
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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 25 May 2011, 06:47
Step 1:
x^4+y^4<10,000

x^4 will be maximum when y^4 is minimum. y^4 is minimum when y=1 because y should be a positive integer.


Step 2:

x^4+1^4<10,000
=> x^4+1<10,000
=>x^4<10,000-1
=>x^4<9,999

Lets substitute x=10, i.e 10*10*10*10 = 10,000

So the value of x should be less than 10 i.e 8. It can't be 9 because no answer choice has 9.


So the answer is option (C)

Last edited by mba4viplav on 25 May 2011, 10:50, edited 1 time in total.

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 25 May 2011, 07:08
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to the two people who picked D is the answer. We both did the work the same way. We agree x < 10.

So why D?

D claims that x can be 9,10,11,12. Which it can't be. So unless I am misunderstanding something, I will stick with my answer of C which says x must be less than 10

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 25 May 2011, 07:51
Seems some problem with the question especially RHS.

x and y being positive integers y #0 and other values of x do not give an integer y value other than x=0.
Hence the question needs to be checked.
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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 25 May 2011, 15:13
The question is from Jeff Sackmann's challenge series. I think OA provided was D which is why I posted it here. I agree that the and should be C.

Posted from my mobile device

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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New post 25 May 2011, 20:17
dreambeliever wrote:
If x and y are positive integers and x^4 + y^4< 10,000, 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


If it is "inclusive": C and D both are the answers.
If it is "exclusive": None of the above.
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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea [#permalink]

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea   [#permalink] 26 Sep 2017, 04:40
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If x and y are positive integers and x^4 + y^4 < 10,000, then the grea

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