$\frac{\left(3^{-1}+4^{-1}\right)^{-2}}{\frac{4^2}{7^2}}=$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

$\frac{\left(3^{-1}+4^{-1}\right)^{-2}}{\frac{4^2}{7^2}}=$

by Gmat_mission » Sun May 05, 2019 10:31 am

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$$\frac{\left(3^{-1}+4^{-1}\right)^{-2}}{\frac{4^2}{7^2}}=$$ A. $\frac{12}{9}$

B. $\frac{49}{144}$

C. $\frac{12}{7}$

D. $7$

E. $9$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun May 05, 2019 10:31 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun May 12, 2019 6:12 pm

Gmat_mission wrote:$$\frac{\left(3^{-1}+4^{-1}\right)^{-2}}{\frac{4^2}{7^2}}=$$ A. $\frac{12}{9}$

B. $\frac{49}{144}$

C. $\frac{12}{7}$

D. $7$

E. $9$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Simplifying the numerator we have:

(1/3 + 1/4)^-2

(4/12 + 3/12)^-2

(7/12)^-2 = (12/7)^2 = 12^2/7^2

Now we have:

(12^2/7^2)/(4^2/7^2)

12^2/4^2 = (12/4)^2 = 9

Answer: E

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