1996 AJHSME Problems/Problem 15

Problem

The remainder when the product $1492\cdot 1776\cdot 1812\cdot 1996$ is divided by 500 is

$\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 4$

Solution

To determine a remainder when a number is divided by $5$, you only need to look at the last digit. If the last digit is $0$ or $5$, the remainder is $0$. If the last digit is $1$ or $6$, the remainder is $1$, and so on.

To determine the last digit of $1492\cdot 1776\cdot 1812\cdot 1996$, you only need to look at the last digit of each number in the product. Thus, we compute $2\cdot 6\cdot 2\cdot 6 = 12^2 = 144$. The last digit of the number $1492\cdot 1776\cdot 1812\cdot 1996$ is also $4$, and thus the remainder when the number is divided by $5$ is also $4$, which gives an answer of $\boxed{E}$.mmm

See Also

1996 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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
All AJHSME/AMC 8 Problems and Solutions

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