If x and y are positive integers and x^4 + y^4

Question

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

pushpitkc · Answer

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)

Archit3110 · Answer

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

ScottTargetTestPrep · Answer

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.

Answer: C.

ajdevgmat · Answer

Wouldn't 9 fall between '9 and 12' also if we are considering inclusive of both values? Or is that not how we see this?

Bunuel · Answer

You are right that if both endpoints were treated as inclusive, 9 would fit both “6 and 9” and “9 and 12.” So the wording is not ideal. The greatest possible value of x is 9, and the intended answer is C, but the choices should be written more clearly to avoid the endpoint ambiguity.

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

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