Question

Nick has to pack 345 candies. In which of the following cases, will some candies be left over after Nick is done packing?
Note: There can be more than one correct answer.

• A. When Nick packs 5 candies in each packet
• B. When Nick packs 2 candies in each packet
• C. When Nick packs 4 candies in each packet
• D. When Nick packs 3 candies in each packet

Answer 1

Answer: (B), (C)

When Nick packs 4 candies in each packet

To check the number of candies left after Nick is done packing, we will divide 345 candies into packets of 2, 3, 4, or 5 candies each.

For that, we need to check the divisibility of 345 by 2, 3, 4, or 5.

(i) The last digit of 345 is neither even or zero. Hence, it will not be divisible by 2. Therefore, some candies will be left after packing.

(ii) The sum of digits of 345 is 3 + 4 + 5 = 12, which is divisible by 3. Hence, it will be divisible by 3. Therefore, no candies will be left after packing.

(iii) The number formed by the last two digits of 345 is 45. Since 45 is not divisible by 4, 345 will also not be divisible by 4. Hence, some candies will be left after packing.

(iv) The last digit of 345 is 5, which is divisible by 5. Hence, 345 will be divisible by 5. Therefore, no candies will be left after packing.

Therefore, some candies will be left if Nick packs either 2 or 4 candies in each pack.