Problem Solving

AAPL wrote:Manhattan Prep

The eSoroban device is available in two colors, orange, and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)

OA B

See the self-explanatory image below.



The correct answer: B

Hope this helps!

-Jay
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AAPL wrote:Manhattan Prep

The eSoroban device is available in two colors, orange, and green. In 2013, 60% of the eSoroban devices sold were purchased by women, \(\frac{5}{12}\) of whom purchased the orange device. If an equal number of orange and green eSoroban devices were sold in 2013, what fraction of men who purchased an eSoroban in 2013 purchased the green device?

A. \(\frac{3}{10}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{12}\)

D. \(\frac{1}{2}\)

E. \(\frac{5}{7}\)

OA B

We can let the total number of eSoroban devices sold = 120. So 0.6 x 120 = 72 were sold to women and 0.4 x 120 = 48 were sold to men. Furthermore, 5/12 x 72 = 30 orange devices and 72 - 30 = 42 green devices were sold to women. Since there are 60 orange device and 60 green devices sold, the number of orange devices sold to men is 60 - 30 = 30, and the number of green devices sold to men is 60 - 42 = 18. Therefore, 18/48 = 3/8 of the men purchased the green devices.

Answer: B