Difference between revisions of "2024 AMC 10A Problems/Problem 1"
(→Solution 1) |
MRENTHUSIASM (talk | contribs) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | What is the value of < | + | What is the value of <cmath>9901\cdot101-99\cdot10101?</cmath> |
<math>\textbf{(A)}~2\qquad\textbf{(B)}~20\qquad\textbf{(C)}~200\qquad\textbf{(D)}~202\qquad\textbf{(E)}~2020</math> | <math>\textbf{(A)}~2\qquad\textbf{(B)}~20\qquad\textbf{(C)}~200\qquad\textbf{(D)}~202\qquad\textbf{(E)}~2020</math> | ||
| Line 7: | Line 7: | ||
== Solution 1 == | == Solution 1 == | ||
The likely fastest method will be straight computation. <math>9901\cdot101</math> evaluates to <math>1000001</math> and <math>99\cdot10101</math> evaluates to <math>999999</math>. The difference is <math>\boxed{\textbf{(A) }2}.</math> | The likely fastest method will be straight computation. <math>9901\cdot101</math> evaluates to <math>1000001</math> and <math>99\cdot10101</math> evaluates to <math>999999</math>. The difference is <math>\boxed{\textbf{(A) }2}.</math> | ||
| + | |||
Solution by [[User:Juwushu|juwushu]]. | Solution by [[User:Juwushu|juwushu]]. | ||
Revision as of 15:15, 8 November 2024
Problem
What is the value of ![\[9901\cdot101-99\cdot10101?\]](http://latex.artofproblemsolving.com/1/3/4/134a62dd445139bc0163af4dc4a59a4de7086e6e.png)
Solution 1
The likely fastest method will be straight computation. 
evaluates to 
and 
evaluates to 
. The difference is 
Solution by juwushu.
See also
| 2024 AMC 10A (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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
