Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 2"
(Created page with "== Problem == Three distinct even positive integers are chosen between <math>1</math> and <math>100,</math> inclusive. What is the largest possible average of these three int...") |
Mathdreams (talk | contribs) (→Solution 2) |
||
| (7 intermediate revisions by 3 users not shown) | |||
| Line 5: | Line 5: | ||
== Solution == | == Solution == | ||
| − | + | The three biggest distinct positive integers that are <math>100</math> or less are <math>100</math>, <math>98</math>, and <math>96</math>. Thus, our answer is <math>\frac{100+98+96}{3} = \boxed{98}</math>. | |
| + | |||
| + | ~Bradygho | ||
| + | |||
| + | == Solution 2 == | ||
| + | |||
| + | Notice that the average of <math>3</math> numbers that form an arithmetic progression is the median of the numbers. Also, notice that to maximize the average of three numbers, we need to maximize the numbers themselves. Using these observations, it is obvious the answer is <math>\boxed{98}</math>. | ||
| + | |||
| + | ~Mathdreams | ||
| + | |||
| + | ==See also== | ||
| + | #[[2021 JMPSC Accuracy Problems|Other 2021 JMPSC Accuracy Problems]] | ||
| + | #[[2021 JMPSC Accuracy Answer Key|2021 JMPSC Accuracy Answer Key]] | ||
| + | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
| + | {{JMPSC Notice}} | ||
Latest revision as of 12:11, 13 July 2021
Contents
Problem
Three distinct even positive integers are chosen between 
and 
inclusive. What is the largest possible average of these three integers?
Solution
The three biggest distinct positive integers that are 
or less are , 
, and 
. Thus, our answer is 
.
~Bradygho
Solution 2
Notice that the average of 
numbers that form an arithmetic progression is the median of the numbers. Also, notice that to maximize the average of three numbers, we need to maximize the numbers themselves. Using these observations, it is obvious the answer is 
.
~Mathdreams
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition. 
