dreamv wrote:If x and y are positive, which of the following must be greater than 1/square root(x+y)?
I. Square root(x+y)/2x
II. (Square root x + square root y)/x+y
III. (square root x - square root y)/x+y
A. I only
B. II only
C. III only.
D. I and II
E. I, II and III
Let x=1 and y=1.
1/√(x+y) = 1/√(1+1) = 1/√2.
Eliminate any expression not greater than 1/√2.
Scanning options I, II and III, we can quickly see that the numerator of III is equal to 0:
(√x-√y)/(x+y) = (√1-√1)/(1+1) = 0.
Eliminate any answer choice that includes III (C and E).
I: √(x+y)/2x
√(1+1)/(2*1) > 1/√2
√2/2 > 1/√2.
Cross-multiplying, we get:
√2 *√2 > 2*1
2>2.
Doesn't work.
Eliminate any remaining answer choice that includes I (A and D).
The correct answer is
B.
Last edited by
GMATGuruNY on Mon Jan 15, 2018 5:45 am, edited 1 time in total.
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