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Difference between revisions of "2024 AMC 8 Problems/Problem 1"

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==Solution 1==
 
==Solution 1==
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We can rewrite the expression as <cmath>222,222-(22,222+2,222+222+22+2)</cmath>.
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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>.
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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.
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~ Dreamer1297
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==Solution 2==
  
 
<cmath>222,222-22,222-2,222-222-22-2</cmath>
 
<cmath>222,222-22,222-2,222-222-22-2</cmath>
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~ nikhil
 
~ nikhil
 
~ CXP
 
~ CXP
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−
==Solution 2==
 
−
 
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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 15:14, 25 January 2024

Problem

What is the ones digit of \[222,222-22,222-2,222-222-22-2?\] $\textbf{(A) } 0\qquad\textbf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8$

Solution 1

We can rewrite the expression as \[222,222-(22,222+2,222+222+22+2)\].

We note that the units digit of the addition is $0$ because all the units digits of the five numbers are $2$ and $5*2=10$, which has a units digit of $0$.

Now, we have something with a units digit of $0$ subtracted from $222,222$. The units digit of this expression is obviously $2$, and we get $\boxed{B}$ as our answer.

~ Dreamer1297


Solution 2

\[222,222-22,222-2,222-222-22-2\] \[= 200,000 - 2,222 - 222 - 22 - 2\] \[= 197778 - 222 - 22 - 2\] \[= 197556 - 22 - 2\] \[= 197534 - 2\] \[= 197532\] This means the ones digit is $\boxed{(B) \hspace{1 mm} 2}$ $\newline$ ~ nikhil ~ CXP

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