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
The United States mint produces coins in 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent denominations. If a jar contains
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Solution:VJesus12 wrote: ↑Wed Jun 24, 2020 3:07 amThe 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
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
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I have a query regarding the language of the question.
The question stem says, "If a jar contains exactly 100 cents worth of THESE COINS".
Doesn't that mean all the denominations have to be there to make the sum up to exactly 100 cents?
The wording is so confusing.
The question stem says, "If a jar contains exactly 100 cents worth of THESE COINS".
Doesn't that mean all the denominations have to be there to make the sum up to exactly 100 cents?
The wording is so confusing.