2009 AMC 12A Problems/Problem 4
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- The following problem is from both the 2009 AMC 12A #4 and 2009 AMC 10A #2, so both problems redirect to this page.
Problem
Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. Which of the following could not be the total value of the four coins, in cents?
Solution
As all five options are divisible by 
, we may not use any pennies. (This is because a penny is the only coin that is not divisible by , and if we used between 
and 
pennies, the sum would not be divisible by .)
Hence the smallest coin we can use is a nickel, and thus the smallest amount we can get is 
. Therefore the option that is not reachable is 
.
We can verify that we can indeed get the other ones:
See Also
| 2009 AMC 12A (Problems • Resources) | ||
| Preceded by Problem 3 | Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| 2009 AMC 10A (Problems • Resources) | ||
| Preceded by Problem 1 | Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
