Quiz (Chinese Remainder Theorem)

(1) Solve the following systems of simultaneous congruences:


(2) Solve the linear congruence by solving the system



(3) Old McDonald collected $75 at the market by selling chickens and geese. He got $4 for each chicken and $7 for each goose. How many of each did he sell?

(4) The basket-of-eggs problem is often phrased in the following terms: One egg remains when the eggs are removed from the basket or at a time; but no eggs remain if they are removed 7 at a time. Find the smallest number of eggs that could have been in the basket.

(5) A certain integer between and leaves the remainder when divided by respectively. What is the integer?

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Cite this as:
Chinese Remainder Theorem Quiz
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/chinese-remainder-theorem-quiz.html