Problem Solving

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?

2

3

4

625

2,087,008,000

As only widgets weighs 5 pounds, all the 5s in the product of the weights must come from widgets only.

Power of 5 in 10,435,040,000
= Power of 5 in (1043504*10000)
= Power of 5 in 10000
= Power of 5 in 10�
= Power of 5 in (2*5)�
= Power of 5 in 5�
= 4

So, 4 widgets have been unloaded.

C