1967 AHSME Problems/Problem 22
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Problem
For natural numbers, when is divided by
, the quotient is
and the remainder is
. When
is divided by
, the quotient is
and the remainder is
. Then, when
is divided by
, the remainder is:
Solution
We are given and
.
Plugging the second equation into the first yields:
If we divide by
, the quotient would be
, and the remainder would be
, which is option
.
See also
1967 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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