1959 AHSME Problems/Problem 13
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The arithmetic mean (average) of a set of numbers is
. If two numbers, namely,
and
, are discarded, the mean of the remaining set of numbers is:
Solution
Since the arithmetic mean of the numbers is
, their sum must be
. After
and
are discarded, the sum decreases by
, so it must become
.
But this means that the new mean of the remaining
numbers must be
. Thusly, our answer is
, and we are done.
See also
1959 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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