Difference between revisions of "1993 UNCO Math Contest II Problems/Problem 5"

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A collection of <math>25</math> consecutive positive integers adds to <math>1000.</math> What are the smallest and largest integers in this collection?
 
A collection of <math>25</math> consecutive positive integers adds to <math>1000.</math> What are the smallest and largest integers in this collection?
 
  
 
== Solution ==
 
== Solution ==

Latest revision as of 20:39, 5 August 2020

Problem

A collection of $25$ consecutive positive integers adds to $1000.$ What are the smallest and largest integers in this collection?

Solution

The thirteenth integer is the average, which is $\frac{1000}{25}=40$. So, the largest integer is 12 larger, which is $40+12=\boxed{52}$, and the smallest integer is 12 less, which is $40-12=\boxed{28}$.

See also

1993 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
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