Question 20
Simon was given a number and asked to divide it by 120. He divided the number by 5,6 and 7 and got 3,2 and 2 as remainders respectively. The remainder when the number is divided by 120 is
Correct Answer: 43
Solution
Dividing successively by 5, 6 and 7 with remainders 3, 2 and 2 means the number has the form $$210k + 73$$. As the number was meant to be divided by 120, it exceeds 120, and the first such value is $$210 + 73 = 283$$. Since $$283 = 2 \times 120 + 43$$, the remainder is 43.
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