1975 AHSME Problems/Problem 6

Revision as of 16:52, 19 January 2021 by Hashtagmath (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

The sum of the first eighty positive odd integers subtracted from the sum of the first eighty positive even integers is

$\textbf{(A)}\ 0 \qquad  \textbf{(B)}\ 20 \qquad  \textbf{(C)}\ 40 \qquad  \textbf{(D)}\ 60 \qquad  \textbf{(E)}\ 80$


Solution

Solution by e_power_pi_times_i


When the $n$th odd positive integer is subtracted from the $n$th even positive integer, the result is $1$. Therefore the sum of the first eighty positive odd integers subtracted from the sum of the first eighty positive even integers is $80\cdot1 = \boxed{\textbf{(E) } 80}$.

See Also

1975 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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 26 27 28 29 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS