GMAT Data Sufficiency (DS) | Re: If x and y are positive, is x^(1/2) + y^(1/2) > 1?

stmt-1:

\sqrt{x + y} > 1

x = 0.10
y = 0.99

x+y = 1.09

sqrt of any number greater than 1 will be greater than the numberitself.

sufficient

stmt-2:
x > y > 1/4

sqrt of 1/4 is 1/2

if both x and y are 1/4 then 1/2 + 1/2 will be EQUAL TO 1. observe that 1/4 < 1/2 but sqrt of 1/4 = 1/2 > 1/4

if y and x are both greater than 1/4 then their roots will be greater than 1/2. sum of two values greater than 1/2 will be > 1.

sufficient

Trick/Pattern/Takeaway: If a number is between 0
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