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This problem trains for: Math Kangaroo 5-6, Math Kangaroo 7-8, SAT-I, GMAT, AMC-8.
In a parking meter there are q quarters, d dimes and n nickels. The number of nickels is one more than twice the number of dimes. The number of quarters is one more than twice the number of nickels. If the total amount is expressed in cents, which of the following could be the last digit of the number of cents?
Denote by n the number of nickels, by d the number of dimes and by c the number of cents.
From the statement we find that there is an odd number of nickels, regardless how many dimes there are:
Similarly, there is an odd number of quarters:
Any number of dimes will give a value that ends in zero.
An odd number of quarters will add up to a value that ends in '5'.
An odd number of nickels will add up to a value that ends in '5'.
The sum of this combination of coins is a number that ends in '0'.