IPM 2012 Mega Final

The teacher writes all the odd numbers less than 100 on the board. How many numbers did she write on the board?

• 15
• 50
• 45
• 90

The numbers 72, 8, 24, 10, 5, 45, 36 and 15 are grouped in pairs so that the product of each pair is the same. What number is paired with 15?

• 72
• 8
• 45
• 24

Father's birthday is celebrated on a Sunday in a certain year. A few months later Mother's birthday is also celebrated on a Sunday. After how many days from father's birthday could mother's birthday have been celebrated?

• 53 days
• 117 days
• 224 days
• 135 days

In how many different ways can the number 50 be represented as the sum of two even natural numbers?

• 14
• 25
• 16
• 12

Rohan has some bags and in each bag he has 3 balls. His friend gives him one ball. Rohan now removes all the balls from the bag and then puts 4 balls in each bag. Now one of the bags is empty. How many balls and bags does he have?

• 3 bags and 12 balls
• 5 bags and 12 balls
• 5 bags and 16 balls
• 4 bags and 12 balls

The bases of four equilateral triangles are sides of a square. Four circles of radius 2 cm are inscribed in the square as shown in the figure. What is the perimeter of the resulting four-corner star?

• 64 cm

• 48 cm

• 96 cm

• 32 cm

One angle of the triangle is three times the second, the third angle is 60⁰. The smallest angle of this triangle is?

• 60⁰
• 30⁰
• 50⁰
• 20⁰

The number 503 is a prime number. How many natural numbers are factors of 2012?

• 2
• 3
• 6
• 8

All four scales are balanced. One possible replacement for '?' is:

• 
• 
• 
• 

In the addition of the three-digit numbers shown, the letters A, P, T, X and E each represent a single digit. Find the value of A + P + T + X + E.

• 21
• 32
• 24
• 34