The United States mint produces coins in 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent denominations. If a jar contains

VJesus12 wrote: ↑

Wed Jun 24, 2020 3:07 am

The United States mint produces coins in 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent denominations. If a jar contains exactly 100 cents worth of these coins, which of the following could be the total number of coins in the jar?

I. 91
II. 81
III. 76

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

[spoiler]OA=D[/spoiler]

Source: Official Guide

Solution:

We can have one 25-cent coin and seventy-five 1-cent coins. So the total number of coins could be 76.

We also can have one 10-cent coin and ninety 1-cent coins. So the total number of coins could be 91.

However, we can’t have a total of 81 coins. That is because the number of 1-cent coins has to be a multiple of 5. If we have eighty 1-cent coins, we need at least two more coins in the other denominations (for example, two 10-cent coins, or, one 10-cent coin and two 5-cent coins). If we have seventy-five 1-cent coins, we need at most five more coins in the other denominations (for example, five 5-cent coins, or two 10-cent coins and one 5-cent coin).

Answer: D