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If 0.01<x<0.02, 1,000<y<5,000, which of the foll

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by Max@Math Revolution » Mon Jan 18, 2016 9:02 pm
If 0.01<x<0.02, 1,000<y<5,000, which of the following can be the value of(x^2y+xy^2)/x^2y^2?

A. 0.2
B. 0.5
C. 75
D. 525
E. 725


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by GMATinsight » Wed Jan 20, 2016 6:05 am
Max@Math Revolution wrote:If 0.01<x<0.02, 1,000<y<5,000, which of the following can be the value of(x^2y+xy^2)/x^2y^2?

A. 0.2
B. 0.5
C. 75
D. 525
E. 725


* A solution will be posted in two days.
to find out the possible values of given expression, Is best to find the range of the values

(x2y+xy2)/x2y2 = xy(x+y)/x2y2 = (x+y)/xy

Min. value of (x+y)/xy = (1/x)+(1/y) = (1/0.02)+(1/5000) = 50.0002

Max. value of (x+y)/xy = (1/x)+(1/y) = (1/0.01)+(1/1000) = 100.0001

Answer: Option C
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by Max@Math Revolution » Wed Jan 20, 2016 8:50 pm
If 0.01<x<0.02, 1,000<y<5,000, which of the following can be the value of(x^2y+xy^2)/x^2y^2?

A. 0.2 B. 0.5 C. 75 D. 525 E. 725


-> (x^2y+xy^2)/x^2y^2=(1/y)+(1/x). Since y is bigger, 1/y is nearly 0. Therefore, you need to figure out 1/x. 1/0.02<1/x<1/0.01 is derived from 0.01<x<0.02. From 50<1/x<100, 75 is the answer. Therefore, the answer is C.
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