Find relation between sum of square roots?

Question

If $x=\sqrt{11}+\sqrt{20}$, $y=\sqrt{15}+\sqrt{17}$ and $z=\sqrt{14}+\sqrt{18}$, then which of the following holds true?

• A. x < y < z
• B. y < z < x
• C. y < x < z
• D. x < z < y
• E. None of these

Please can anyone tell me how to solve this problem in Aptitude point of view

Answer 1

$x^2=31+2\sqrt{220}$

$y^2=32+2\sqrt{255}$

$z^2=32+2\sqrt{252}$

Answer 2

Note that $x<\sqrt{12}+\sqrt{20}$ and $\sqrt{x}$ is concave.

By the majorization inequality, we get $x<z<y$.