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Difference between revisions of "2024 AMC 10B Problems/Problem 5"

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{{duplicate|[[2024 AMC 10B Problems/Problem 5|2024 AMC 10B #5]] and [[2024 AMC 12B Problems/Problem 5|2024 AMC 12B #5]]}}
  
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==Problem==
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In the following expression, Melanie changed some of the plus signs to minus signs:
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<cmath>1+3+5+7+...+97+99</cmath>
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When the new expression was evaluated, it was negative. What is hte least number of plus signs that Melanie could have changed to minus signs?
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<math>\textbf{(A) } 14 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 16 \qquad\textbf{(D) } 17 \qquad\textbf{(E) } 18</math>
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==Solution 1==
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B) 15, 35^2=1225*2=2450<2500.
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==See also==
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{{AMC10 box|year=2024|ab=B|num-b=3|num-a=5}}
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{{AMC12 box|year=2024|ab=B|num-b=3|num-a=5}}
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{{MAA Notice}}

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: \[1+3+5+7+...+97+99\] When the new expression was evaluated, it was negative. What is hte least number of plus signs that Melanie could have changed to minus signs?

$\textbf{(A) } 14 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 16 \qquad\textbf{(D) } 17 \qquad\textbf{(E) } 18$

Solution 1

B) 15, 35^2=1225*2=2450<2500.

See also

2024 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 3 		Followed by
Problem 5
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 3 		Followed by
Problem 5
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. AMC logo.png

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