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

m (→‎Solution 2)
(→‎Solution 2)
Line 27: Line 27:
 
==Solution 2==
 
==Solution 2==
  
−
<math>222,222-22,222 = 200,000
+
<math>222,222-22,222 = 200,000</math>
−
200,000 - 2,222 = 197778
+
<math>200,000 - 2,222 = 197778</math>
−
197778 - 222 = 197556
+
<math>197778 - 222 = 197556</math>
−
197556 - 22 = 197534
+
<math>197556 - 22 = 197534</math>
−
197534 - 2 = 1957532
+
<math>197534 - 2 = 1957532
 
</math>
 
</math>
 
So our answer is <math>\boxed{\textbf{(B) } 2}</math>.
 
So our answer is <math>\boxed{\textbf{(B) } 2}</math>.

Revision as of 19:36, 24 July 2024

Problem 1

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

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.

−


−

Solution 2

$222,222-22,222 = 200,000$ $200,000 - 2,222 = 197778$ $197778 - 222 = 197556$ $197556 - 22 = 197534$ $197534 - 2 = 1957532$ So our answer is $\boxed{\textbf{(B) } 2}$.

Solution 3

We only care about the unit's digits.

Thus, $2-2$ ends in $0$, $0-2$ ends in $8$, $8-2$ ends in $6$, $6-2$ ends in $4$, and $4-2$ ends in $\boxed{\textbf{(B) } 2}$.

Solution 4

We just take the units digit of each and subtract, or you can do it this way by adding an extra ten to the first number (so we don't get a negative number): \[12-2-(2+2+2+2)=10-8=2\] Thus, we get the answer $\boxed{(B)}$

Video Solution 1 (Quick and Easy!)

https://youtu.be/Ol1seWX0xHY

~Education, the Study of Everything

Video Solution (easy to understand)

https://youtu.be/BaE00H2SHQM?si=O0O0g7qq9AbhQN9I&t=130

~Math-X

Video Solution by Interstigation

https://youtu.be/ktzijuZtDas&t=36

Video Solution by Daily Dose of Math

https://youtu.be/bSPWqeNO11M?si=HIzlxPjMfvGM5lxR

~Thesmartgreekmathdude

See Also

2024 AMC 8 (Problems • Answer Key • Resources)
Preceded by
First Problem 		Followed by
Problem 2
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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