Difference between revisions of "2021 AMC 10A Problems/Problem 22"
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==Problem== | ==Problem== | ||
| + | Hiram's algebra notes are <math>50</math> pages long and are printed on <math>25</math> sheets of paper; the first sheet contains pages <math>1</math> and <math>2</math>, the second sheet contains pages <math>3</math> and <math>4</math>, and so on. One day he leaves his notes on the table before leaving for lunch, and his roommate decides to borrow some pages from the middle of the notes. When Hiram comes back, he discovers that his roommate has taken a consecutive set of sheets from the notes and that the average (mean) of the page numbers on all remaining sheets is exactly <math>19</math>. How many sheets were borrowed? | ||
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| + | <math>\textbf{(A)} ~10\qquad\textbf{(B)} ~13\qquad\textbf{(C)} ~15\qquad\textbf{(D)} ~17\qquad\textbf{(E)} ~20</math> | ||
==Solution== | ==Solution== | ||
Revision as of 19:21, 11 February 2021
Problem
Hiram's algebra notes are 
pages long and are printed on 
sheets of paper; the first sheet contains pages 
and 
, the second sheet contains pages 
and 
, and so on. One day he leaves his notes on the table before leaving for lunch, and his roommate decides to borrow some pages from the middle of the notes. When Hiram comes back, he discovers that his roommate has taken a consecutive set of sheets from the notes and that the average (mean) of the page numbers on all remaining sheets is exactly 
. How many sheets were borrowed?
Solution
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See also
| 2021 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 | ||
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