Difference between revisions of "2024 AMC 10B Problems/Problem 5"
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In the following expression, Melanie changed some of the plus signs to minus signs: | In the following expression, Melanie changed some of the plus signs to minus signs: | ||
<cmath>1+3+5+7+...+97+99</cmath> | <cmath>1+3+5+7+...+97+99</cmath> | ||
| − | When the new expression was evaluated, it was negative. What is | + | When the new expression was evaluated, it was negative. What is the least number of plus signs that Melanie could have changed to minus signs? |
<math>\textbf{(A) } 14 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 16 \qquad\textbf{(D) } 17 \qquad\textbf{(E) } 18</math> | <math>\textbf{(A) } 14 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 16 \qquad\textbf{(D) } 17 \qquad\textbf{(E) } 18</math> | ||
Revision as of 00:38, 14 November 2024
- The following problem is from both the 2024 AMC 10B #5 and 2024 AMC 12B #5, so both problems redirect to this page.
Problem
In the following expression, Melanie changed some of the plus signs to minus signs:
![\[1+3+5+7+...+97+99\]](http://latex.artofproblemsolving.com/a/3/0/a307bbc8aeccf32d5dea44474103639a57f21408.png)
When the new expression was evaluated, it was negative. What is the least number of plus signs that Melanie could have changed to minus signs?
Solution 1
B) 15, 35^2=1225*2=2450<2500.
See also
| 2024 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 | ||
| 2024 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 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 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
