Just use the same cross-multiply approach which you use when you compare numbers.
For e.g to compare which one is greater 2/3 or 3/4, you multiply 2*4 & 3*3.
Use the same approach. Also as soon as you find an option which is greater, just stop. You don't have to test every answer.
If x and y are positive, which of the following ...
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Source: Beat The GMAT — Problem Solving |
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cramya
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I think I posted my solution before for this.
Since sqrt(x+y),sqrt(x) and sqrt(y) are present take x=16 y=9
Their sum 16+9 = 25 is also a pefect square
This makes the computations simple and fool proof!
Since sqrt(x+y),sqrt(x) and sqrt(y) are present take x=16 y=9
Their sum 16+9 = 25 is also a pefect square
This makes the computations simple and fool proof!
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parallel_chase
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My approach is algebraic in solving such questions.
important keywords = "must" + "positive"
1/sqrt(x+y) = sqrt(x+y)/(x+y)
I. sqrt(x+y)/2x, if x and y have the same value sqrt(x+y)/(x+y) = sqrt(x+y)/2x - eliminate
II. sqrtx+sqrty/(x+y) III. sqrtx - sqrty/(x+y)
The denominator of two options is same as that of question stem, therefore, option whose numerator is greatest must be greater.
if x and y are positive sqrtx + sqrt y will always be greater than sqrt(x+y)
Hence II only.
Hope this helps.
important keywords = "must" + "positive"
1/sqrt(x+y) = sqrt(x+y)/(x+y)
I. sqrt(x+y)/2x, if x and y have the same value sqrt(x+y)/(x+y) = sqrt(x+y)/2x - eliminate
II. sqrtx+sqrty/(x+y) III. sqrtx - sqrty/(x+y)
The denominator of two options is same as that of question stem, therefore, option whose numerator is greatest must be greater.
if x and y are positive sqrtx + sqrt y will always be greater than sqrt(x+y)
Hence II only.
Hope this helps.
No rest for the Wicked....
