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If 0.001 < a < 0.002 and 1,000 < b < 2,000, whic

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If 0.001 < a < 0.002 and 1,000 < b < 2,000, whic

by Max@Math Revolution » Fri Jun 07, 2019 12:55 am

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[GMAT math practice question] 6.7

If 0.001 < a < 0.002 and 1,000 < b < 2,000, which of the following could be the value of a^3b^2+a^2b^3/a^3b^3?

A. 15
B. 125
C. 625
D. 1250
E. 6250
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by Max@Math Revolution » Sun Jun 09, 2019 5:13 pm
=>

$$\frac{a^3b^2+a^2b^3}{a^3b^3}=\frac{1}{a}+\frac{1}{b}$$

Since 0.001 < a < 0.002 and 1,000 < b < 2,000, we have 500 < 1/a < 1000 and 1/2000 < 1/b < 1/1000.
Thus

$$500+\frac{1}{2000}\ <\ \frac{a^3b^2+a^2b^3}{a^3b^3}\ <\ 1000+\frac{1\ }{1000}$$

Therefore, C is the only possible answer.
Answer: C
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