Difference between revisions of "2006 AMC 8 Problems/Problem 24"
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<math>CDCD = CD \cdot 101</math>, so <math>ABA = 101</math>. Therefore, <math>A = 1</math> and <math>B = 0</math>, so <math>A+B=1+0=\boxed{\textbf{(A)}\ 1}</math>. | <math>CDCD = CD \cdot 101</math>, so <math>ABA = 101</math>. Therefore, <math>A = 1</math> and <math>B = 0</math>, so <math>A+B=1+0=\boxed{\textbf{(A)}\ 1}</math>. | ||
+ | |||
+ | |||
+ | ==Solution 2== | ||
+ | |||
+ | Method 1: Test examples | ||
+ | Method 2: When you do bash: | ||
+ | |||
+ | <math>(100A+10B+A)(10C+D) = 100C+100D+10C+D</math> | ||
+ | <math>100AC+100BC+100AC+100AD+10BD+AD=1010C+101D</math> | ||
+ | <math>1010(A-1)(C) + 101(A-1)D + 100CB+10D=0</math> | ||
+ | <math>A=1</math> | ||
+ | <math>D=0</math> | ||
+ | <math>B=0</math> | ||
+ | |||
+ | And now 0+1=2. I mean, 1. So the answer is \boxed{\textbf{(A)} | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2006|n=II|num-b=23|num-a=25}} | {{AMC8 box|year=2006|n=II|num-b=23|num-a=25}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 01:07, 6 June 2021
Problem
In the multiplication problem below ,
,
,
and are different digits. What is
?
Video solution
https://youtu.be/sd4XopW76ps -Happytwin
https://youtu.be/7an5wU9Q5hk?t=3080
https://www.youtube.com/channel/UCUf37EvvIHugF9gPiJ1yRzQ
Solution
, so
. Therefore,
and
, so
.
Solution 2
Method 1: Test examples Method 2: When you do bash:
And now 0+1=2. I mean, 1. So the answer is \boxed{\textbf{(A)}
See Also
2006 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.