gmatbusters wrote:

On each of the first three days of the month, Danny ate twice the number of apples he had eaten the day before. The ratio of the number of apples he ate on the third day to the number he ate on the fourth day is \(\frac{3}{5}\). What is the ratio of the number of apples Danny ate on the second day of the month to the number he ate on the fourth day?

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

B) \(\frac{3}{20}\)

C) \(\frac{1}{2}\)

D) \(\frac{6}{5}\)

E) \(\frac{10}{3}\)

Since the ratio of the number of apples he ate on the third day to the number he ate on the fourth day is 3/5 and he ate half as many apples on the second day as on the third day, he must have eaten 1 ½, or 3/2 apples on the second day. Thus, the ratio of the number of apples he ate on the second day to the number he ate on the fourth day is 3/2 / 5 = 3/2 x 1/5 = 3/10.

Alternate Solution:

Let the number of apples Danny ate on the first day be x. Then, in the second and third days, he ate 2x and 4x apples, respectively. Since the ratio of the apples he ate on the third day to the number he ate on the fourth day is 3/5, he ate 4x/(3/5) = 20x/3 apples on the fourth day. Thus, the ratio of the number of apples Danny ate on the second day to the number he ate on the fourth day is (2x)/(20x/3) = 6/20 = 3/10.

Answer: A

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