Difference between revisions of "1998 CEMC Gauss (Grade 7) Problems/Problem 2"

(Created page with "== Problem == The number <math>4567</math> is tripled. The ones digit (units digit) in the resulting number is <math>\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7...")
 
 
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<math>\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 1</math>
 
<math>\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 1</math>
  
== Solution ==
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== Solution 1==
 
Multiply: <math>4567 \cdot 3 = 13701.</math> The units digit is the rightmost digit, which is 1.  
 
Multiply: <math>4567 \cdot 3 = 13701.</math> The units digit is the rightmost digit, which is 1.  
  
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-edited by coolmath34
 
-edited by coolmath34
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== Solution 2==
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The units digit of a product only depends on the units digits of the numbers being multiplied, which reduces the problem down to <math>7 \cdot 3 = 21</math>, meaning that the units digit is 1 and the answer is <math>\boxed{E}</math>.

Latest revision as of 15:14, 15 June 2022

Problem

The number $4567$ is tripled. The ones digit (units digit) in the resulting number is

$\text{(A)}\ 5 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ 1$

Solution 1

Multiply: $4567 \cdot 3 = 13701.$ The units digit is the rightmost digit, which is 1.

The answer is $\boxed{E}.$

-edited by coolmath34

Solution 2

The units digit of a product only depends on the units digits of the numbers being multiplied, which reduces the problem down to $7 \cdot 3 = 21$, meaning that the units digit is 1 and the answer is $\boxed{E}$.