Difference between revisions of "2013 AMC 8 Problems/Problem 17"
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==Solution 1== | ==Solution 1== | ||
| − | The arithmetic mean of these numbers is <math>\frac{\frac{2013}{3}}{2}=\frac{671}{2}=335.5</math>. Therefore the numbers are <math>333</math>, <math>334</math>, <math>335</math>, <math>336</math>, <math>337</math>, <math>338</math>, so the answer is <math>\boxed{\textbf{(B)}\ 338}</math> | + | The arithmetic mean of these numbers is <math>\frac{\frac{2013}{3}}{2}=\frac{671}{2}=335.5</math>. Therefore the numbers are <math>333</math>, <math>334</math>, <math>335</math>, <math>336</math>, <math>337</math>, <math>338</math>, so the answer is <math>\boxed{\textbf{(B)}\ 338}</math>. |
==Solution 2== | ==Solution 2== | ||
Latest revision as of 16:08, 23 December 2024
Contents
[hide]Problem
The sum of six consecutive positive integers is 2013. What is the largest of these six integers?
Solution 1
The arithmetic mean of these numbers is 
. Therefore the numbers are 
, 
, 
, 
, 
, 
, so the answer is 
.
Solution 2
Let the 
number be 
. Then our desired number is 
.
Our integers are 
, so we have that 
.
Solution 3
Let the first term be . Our integers are 
. We have, 
.
Solution 4
Since there are 
numbers, we divide 
by to find the mean of the numbers. 
.
Then, 
(the fourth number). Fifth: ; Sixth: 
.
Solution 5
Let the 
number be . Then our list is: 
. Simplifying this gets you 
, which means that 
.
Video Solution by Pi Academy
https://youtu.be/KDEq2bcqWtM?si=M5fwa9pAdg1cQu0o
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
