swerve wrote:Every day a certain bank calculates its average daily deposit for that calendar month up to and including that day. If on a randomly chosen day in June the sum of all deposits up to and including that day is a prime integer greater than 100, what is the probability that the average daily deposit up to and including that day contains fewer than 5 decimal places?

A. 1/10
B. 2/15
C. 4/15
D. 3/10
E. 11/30

Recall that a fraction a/b (in lowest terms) can be expressed as a decimal with a finite number of decimal places if and only if b = 1 or b is a product of 2's and/or 5's only.

Here, if we express the average daily deposit up to and including certain day of June as a/b, then a = the sum of all deposits up to and including that day and b = that day in June (notice that 1 ≤ b ≤ 30).

We are given that a is a prime integer greater than 100, so a/b will be in lowest terms. Thus we need to find all the values of b described in the first paragraph. Therefore, b could be:

1, 2, 4 = 2^2, 5, 8 = 2^3, 10 = 2 x 5, 16 = 2^4, 20 = 2^2 x 5, and 25 = 5^2 (note: the next number is 32 = 2^5, but 32 > 30)

We can see that out of the 30 days in June, 9 of them will have the average daily deposit to be a number with fewer than 5 decimal places, so the probability is 9/30 = 3/10.

Answer: D