Interested in seeing the various approaches people take when solving this one.
Thanks.
If x and y are positive, which of the following ...
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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.
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.
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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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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....