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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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Joined: 02 Sep 2009
Posts: 58423
If x and y are positive integers and x^4 + y^4 < 10,000, then the grea  [#permalink]

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22 Feb 2019, 07:15
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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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22 Feb 2019, 07:24
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Bunuel 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

In order to find the greatest value of x, y must be minimum(smallest positive integer is 1)

Equation becomes x^4 < 9999 when y = 1.
Since $$10^4 = 10000$$, the maximum value that x can take is 9

Therefore, the greatest possible value of x is between 6 and 9(Option C)
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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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22 Feb 2019, 09:54
Bunuel 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

at 10^4 = 10,000
from given options we can say that it cannot be option D & E
so best is C between 6 & 9
IMO C
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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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24 Feb 2019, 06:49
Bunuel 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

Since we want to find the greatest possible value of x, we want y to be as small as possible. The smallest y can be is 1. So we have:

x^4 + 1^4 < 10,000

x^4 < 9,999

We see that if x = 10, then x^4 = 10000, which is just 1 more than 9,999. So if x = 9, then 9^4 will certainly be less than 9,999.

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Re: If x and y are positive integers and x^4 + y^4 < 10,000, then the grea   [#permalink] 24 Feb 2019, 06:49
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