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smc

prealgebra senior

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?
(A)
(B)
(C)
(D)
Solution
Note that if we use any pennies whatsoever (one, two, three, or four of them), then the total amount of money would be nonzero mod ; as all five options are divisible by , we conclude that we may not use any pennies. 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:
Final answer
A