One short
A whole number less than 100 gives remainders of 2, 3 and 4 when divided by 3, 4 and 5. What is the remainder when it is divided by 7?
Age
11 to 14
Challenge level
Problem
A positive whole number less than $100$ has remainder $2$ when it is divided by $3$, remainder $3$ when it is divided by $4$ and remainder $4$ when it is divided by $5$. What is its remainder when it is divided by $7$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 3
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The next number is 60
The number is 59
59$\div$7 = 8 remainder 3
(Note that the Chinese Remainder Theorem provides a general method for solving problems like this.)