Difference between revisions of "2021 AMC 12A Problems/Problem 3"
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| − | Since the ones place of a multiple of <math>10</math> is <math>0</math>, this implies the other integer has to end with a <math>2</math> since both integers sum up to a number that ends with a <math>2</math>. Thus, the ones place of the difference has to be <math>10-2=8</math>, and the only answer choice that ends with an <math>8</math> is <math>\boxed{\textbf{(D)~ | + | Since the ones place of a multiple of <math>10</math> is <math>0</math>, this implies the other integer has to end with a <math>2</math> since both integers sum up to a number that ends with a <math>2</math>. Thus, the ones place of the difference has to be <math>10-2=8</math>, and the only answer choice that ends with an <math>8</math> is <math>\boxed{\textbf{(D)}~14328</math> |
~CoolJupiter 2021 | ~CoolJupiter 2021 | ||
Revision as of 21:23, 11 February 2021
Contents
Problem
The sum of two natural numbers is 
. One of the two numbers is divisible by 
. If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?
Solution
The units digit of a multiple of will always be 
. We add a whenever we multiply by . So, removing the units digit is equal to dividing by .
Let the smaller number (the one we get after removing the units digit) be 
. This means the bigger number would be 
.
We know the sum is 
so 
. So 
. The difference is 
. So, the answer is 
.
--abhinavg0627
Solution 2(Lazy Speed)
Since the ones place of a multiple of is , this implies the other integer has to end with a 
since both integers sum up to a number that ends with a . Thus, the ones place of the difference has to be 
, and the only answer choice that ends with an 
is $\boxed{\textbf{(D)}~14328$ (Error compiling LaTeX. Unknown error_msg)
~CoolJupiter 2021
Video Solution by Punxsutawney Phil
https://youtube.com/watch?v=MUHja8TpKGw&t=143s
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
Video Solution (Using Algebra and Meta-solving)
-pi_is_3.14
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
