Difference between revisions of "2024 AMC 8 Problems/Problem 1"
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~nikhil | ~nikhil | ||
| + | ~ CXP | ||
| + | |||
| + | ==Solution 2== | ||
| + | |||
| + | We can rewrite the expression as <cmath>222,222-(22,222+2,222+222+22+2)</cmath>. | ||
| + | |||
| + | We note that the units digit of the addition is <math>0</math> because all the units digits of the five numbers are <math>2</math> and <math>5*2=10</math>, which has a units digit of <math>0</math>. | ||
| − | ~ | + | Now, we have something with a units digit of <math>0</math> subtracted from <math>222,222</math>. The units digit of this expression is obviously <math>2</math>, and we get <math>\boxed{B}</math> as our answer. |
| + | |||
| + | ~ Dreamer1297 | ||
Revision as of 15:13, 25 January 2024
Problem
What is the ones digit of ![\[222,222-22,222-2,222-222-22-2?\]](http://latex.artofproblemsolving.com/e/2/f/e2fbba6a2cccb3d60b70444a8b272999a204281e.png)
Solution 1
![\[222,222-22,222-2,222-222-22-2\]](http://latex.artofproblemsolving.com/a/2/7/a2725dab8150e76bea650e7fe8585ceecf400c33.png)
![\[\equiv 2-2-2-2-2-2\]](http://latex.artofproblemsolving.com/d/b/3/db37d9f234f299d75e5207584906b039abedc379.png)
![\[\equiv -8\]](http://latex.artofproblemsolving.com/2/9/d/29ddd3ce8b10dc0f9a6f36a79d1ad76b5c400abb.png)
![\[\equiv 2\]](http://latex.artofproblemsolving.com/b/1/1/b11d342808f9e78408b144a42636280aa7cf6855.png)
So the solution is 
~nikhil ~ CXP
Solution 2
We can rewrite the expression as ![\[222,222-(22,222+2,222+222+22+2)\]](http://latex.artofproblemsolving.com/7/4/4/7445dae34eda233ea2977782a2fb83b9a63378fc.png)
.
We note that the units digit of the addition is 
because all the units digits of the five numbers are and 
, which has a units digit of .
Now, we have something with a units digit of subtracted from 
. The units digit of this expression is obviously , and we get 
as our answer.
~ Dreamer1297
