chetan2u wrote:
Bunuel wrote:
The square root of integer x is equal to the sum of the cubes of y and z. If the squares of y and z are each less than 10, what is the greatest possible value of x?
A. 2916
B. 3981
C. 3982
D. 3999
E. 4000
Hi...
Let the values be √10 each.
here the values will be just LESS than 10, so our ACTUAL answer will be slightly less than the answer we get here So sum of cubes is \(2*10^{\frac{3}{2}}\)
Square of this is \(4*10^3=4000\)..
But the actual ans will be slightly LESS than 4000 and an integer..
So 3999
D
Chetan - Thanks for responding. Although, I wish you hadn't used "yellow" to highlight the text against an almost yellow background. Nevertheless, here is my approach and I don't know if I arrived at the wrong answer.
Given,
\(\sqrt{x}\) = \(y^3\) + \(z^3\)
And is also given,
\(y^2\) < 10
\(z^2\) < 10
So, the biggest value that y and z could each take is 3. Since, the question asks for the highest value, I have assumed the highest value for y and z (i.e, 3).
\(\sqrt{x}\) = \(3^3\) + \(3^3\)
=> \(\sqrt{x}\) = 27 + 27
=> \(\sqrt{x}\) = 54 and squaring both sides, we get:
x = \({54}^2\)
x = 2916.
Answer = A
Please correct if I am wrong.
Sorry for the colour. Didn't realise it.
You are WRONG when you read it as an integer.
It is nowhere given as an integer.
So if √10=3.16227766.., the value could be 3.16227765..
Hence we find answer by taking it as 10 and finding one value lesser INTEGER.