Difference between revisions of "2024 AMC 10B Problems/Problem 2"
m (Protected "2024 AMC 10B Problems/Problem 2" ([Edit=Allow only administrators] (expires 04:59, 14 November 2024 (UTC)) [Move=Allow only administrators] (expires 04:59, 14 November 2024 (UTC)))) |
|||
| Line 1: | Line 1: | ||
| + | {{duplicate|[[2024 AMC 10B Problems/Problem 2|2024 AMC 10B #2]] and [[2024 AMC 12B Problems/Problem 2|2024 AMC 12B #2]]}} | ||
| + | ==Problem== | ||
| + | What is <math>10! - 7! \cdot 6!</math> | ||
| + | |||
| + | <math>\textbf{(A) } -120 \qquad\textbf{(B) } 0 \qquad\textbf{(C) } 120 \qquad\textbf{(D) } 600 \qquad\textbf{(E) } 720</math> | ||
| + | |||
| + | ==Solution 1== | ||
| + | <math>10! = 10 \cdot 9 \cdot 8 \cdot 7! = 720 \cdot 7!</math> | ||
| + | |||
| + | <math>6! \cdot 7! = 720 \cdot 7!</math> | ||
| + | |||
| + | Therefore, the equation is equal to <math>720 \cdot 7! - 720 \cdot 7! = \boxed{\textbf{(B) }0}</math> | ||
| + | |||
| + | ~ARay10 | ||
| + | |||
| + | ==See also== | ||
| + | {{AMC10 box|year=2024|ab=B|num-b=1|num-a=3}} | ||
| + | {{AMC12 box|year=2024|ab=B|num-b=1|num-a=3}} | ||
| + | {{MAA Notice}} | ||
Revision as of 00:20, 14 November 2024
- The following problem is from both the 2024 AMC 10B #2 and 2024 AMC 12B #2, so both problems redirect to this page.
Problem
What is 
Solution 1
Therefore, the equation is equal to 
~ARay10
See also
| 2024 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 1 |
Followed by Problem 3 |
| 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. 
