1975 AHSME Problems/Problem 6

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 $80\cdot1 = \boxed{\textbf{(E) } 80}$ .

1975 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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1975 AHSME Problems/Problem 6

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