GMAT Prep - Quant 2

[Sumit69]

Dear Ian\Stuart,

Please suggest the best and the quickest way to solve these type of questions.

Rgds,
Sumit

[chetanojha]

Lets pick numbers, since both are positive. Let x=16 and y=9 (i pick perfect squares to its easy to compute values)

you need the answer which is greater than 1/sqrt(x+y). i.e 1/sqrt(16+9)=1/5=>0.2

Now plug the above value of x and y and you will find:

1.sqrt(x+y)/2x=sqrt(16+9)/2*16=>5/32=>0.15 Not correct.

2.sqrt(16)+sqrt(y)/(x+y)=>sqrt(16)+sqrt(9)/(16+9)=>9/25=>0.36 Correct.

3.sqrt(16)-sqrt(y)/(x+y)=>sqrt(16)-sqrt(9)/(16+9) =>1/25 => 0.04 Not correct

Hence answer II only.

[bmlaud]

If you don't want to choose numbers then the best method is to make denominators of the fractions same and compare the numerators.
The fractions reduce down to following comparisons

Option1: Is 2x(sqrt(x+y)) > (x+y)(sqrt(x+y)) => is 2x>(x+y)
True only when x>y - can't say

Option2: Is (sqrt(x) + sqrt(y)) > (sqrt(x+y))
squaring both sides ( x+y+2sqrt(x)sqrt(y)) > (x+y) => yes true

Option3: Is (sqrt(x) - sqrt(y)) > (sqrt(x+y)) ; again squaring both sides
we get ( x+y-2sqrt(x)sqrt(y)) > (x+y) => No

[Vemuri]

My 2 cents.....pick numbers appropriate. Its the fastest way to solve these kind of questions. You don't want to be bogged down by time in the real exam.