A cargo ship carrying four kinds of items, doohickies

Since 2, 11, 5 and 7 are all prime numbers and 10,435,040,000 is a product of all of these numbers, they key here is to prime factorize 10,435,040,000. That may look a little daunting without a calculator but the question is only asking about widgets, so we only need to find how many 5's are factors

10,435,040,000
1,043,504 x 10,000
1,043,504 x 10 $$^4$$
1,043,504 x (2*5) $$^4$$
1,043,504 x 2 $$^4$$ x 5 $$^4$$

Since 1,043,504 doesn't end in a 0 or a 5, we know 5 doesn't go into it. So there are four factors of 5 and the answer is C.

Make sense?

Take care,
Sionainn Marcoux
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

with better formatting:

10,435,040,000
1,043,504 x 10,000
1,043,504 x 10^4
1,043,504 x (2*5)^4
1,043,504 x 2^4 x 5^4

BTGmoderatorLU wrote:A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 10,435,040,000 pounds, how many widgets have been unloaded?

A. 2
B. 3
C. 4
D. 625
E. 2,087,008,000

We can let d, g, w, and y be the number of doohickies, geegaws, widgets, and yamyams respectively and create the following equation:

2^d x 11^g x 5^w x 7^y = 10,435,040,000

Notice that we are asked only for the number of widgets, or the value of w. We observe that 10,435,040,000 has 4 trailing zeros, which means there must be 4 factors of 5 in 10,435,040,000. Thus w must be 4.

Answer: C