which of the following must be greater

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which of the following must be greater

by nikhilsrl » Wed Mar 23, 2011 4:01 am
If x and y are positive, which of the following must be greater that 1/sqrt(x + y)?

I. sqrt(x + y)/2x
II. [sqrt(x) + sqrt(y)]/(x + y)
III. [sqrt(x) - sqrt(y)]/(x + y)

a) None
b) I only
c) II only
d) I and II
e) II and III

OA is D. Is there an easier to solve this than using numbers.
Source: — Problem Solving |

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by HSPA » Wed Mar 23, 2011 4:08 am
Let x= y = 8 => 1/sqrt(x+y) = 1/4

I) sqrt(x+y)/2x = sqrt(16)/16 = 1/4

How is OA D.. I am getting it as C