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Difference between revisions of "1996 AJHSME Problems/Problem 15"

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To determine a remainder when a number is divided by <math>5</math>, you only need to look at the last digit.  If the last digit is <math>0</math> or <math>5</math>, the remainder is <math>0</math>.  If the last digit is <math>1</math> or <math>6</math>, the remainder is <math>1</math>, and so on.
 
To determine a remainder when a number is divided by <math>5</math>, you only need to look at the last digit.  If the last digit is <math>0</math> or <math>5</math>, the remainder is <math>0</math>.  If the last digit is <math>1</math> or <math>6</math>, the remainder is <math>1</math>, and so on.
  
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To determine the last digit of <math>1492\cdot 1776\cdot 1812\cdot 1996</math>, you only need to look at the last digit of each number in the product.  Thus, we compute <math>2\cdot 6\cdot 2\cdot 6 = 12^2 = 144</math>.  The last digit of the number <math>1492\cdot 1776\cdot 1812\cdot 1996</math> is also <math>4</math>, and thus the remainder when the number is divided by <math>5</math> is also <math>4</math>, which gives an answer of <math>\boxed{E}</math>.mmm
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To determine the last digit of <math>1492\cdot 1776\cdot 1812\cdot 1996</math>, you only need to look at the last digit of each number in the product.  Thus, we compute <math>2\cdot 6\cdot 2\cdot 6 = 12^2 = 144</math>.  The last digit of the number <math>1492\cdot 1776\cdot 1812\cdot 1996</math> is also <math>4</math>, and thus the remainder when the number is divided by <math>5</math> is also <math>4</math>, which gives an answer of <math>\boxed{E}</math>.
  
 
==See Also==
 
==See Also==

Revision as of 09:16, 3 December 2022

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 $\boxed{E}$.

See Also

1996 AJHSME (Problems • Answer Key • Resources)
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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