1) Which smallest 3‑digit number is exactly equal to the sum of the cube of its digits?

2) A woman is now four times as old as her daughter and twice as old as her son.
In 6 years, the woman will be three times as old as her daughter.
How old was she when her son was born?

3) A number is divisible by 9 and ends with the digit 0.

Which of the following could be the number?

4) What is the sum of the first 30 natural numbers?

5) A fruit vendor has 120 apples and 90 oranges.
He wants to make identical fruit baskets using all the fruits.

What is the maximum number of baskets he can make?

6) A boy multiplied a number by 5 instead of dividing it by 5.

What is the ratio of the wrong answer to the correct answer?

7) What is the sum of the first 20 natural numbers?

8) Detective Arjun finds a locker in a suspect’s basement.
A sticky note on the locker reads:

“My locker combination is the smallest positive number that
– leaves remainder 0 when divided by 6
– leaves remainder 2 when divided by 8
– leaves remainder 0 when divided by 9
and the product of its digits is 24.”

Only one number satisfies all conditions.

What is the locker combination?

9) A number exceeds its one-third by 56.

What is the number?

10) Which of the following numbers is divisible by both 3 and 11?

11) What smallest number should be added to 1000 so that it becomes divisible by 21?

12) A container has some candies.
The candies can be arranged perfectly into groups of 5 or 8.
But when arranged into groups of 18, there are 2 candies left over.
What is the smallest possible number of candies?

13) A number leaves a remainder 4 when divided by 7,
and a remainder 10 when divided by 13.
What is the smallest such number?

14) If the number 7a5 (where a is a digit) is divisible by 9, what is a?

15) The product of a man’s age and his son’s age is 500.
The man is 5 times as old as his son.
How old is the man?

16) A man is now three times as old as his son and twice as old as his daughter.
In 12 years, the man will be twice as old as his son.
How old was he when his daughter was born?

17) What is the sum of all prime numbers less than 20?

18) If A is the smallest five-digit number formed using all the digits 1, 3, 4, 6, 8 exactly once,
and B is the greatest five-digit number formed using all the digits 0, 2, 5, 7, 9 exactly once,
find B – A.

19) A two-digit number is 4 times the sum of its digits.
Reversing the digits increases the number by 18.
What is the number?

20) The sum of a father and son’s age is 65.
Ten years ago, the product of their ages was a perfect square.
Find the father’s current age.