IPM 2019 Mega Final

The pages of a book are numbered 1, 2, 3, 4 ….. In total it takes 852 digits to number all the pages of the book. What is the number of the last page of this book?

• 284
• 320
• 302
• 248

Rakesh has 5 baskets containing 138 apples. He now adds apples in all 5 baskets as follows. In the 1st basket he adds 2 apples, in the 2nd basket he adds 4 apples, in the 3rd basket he adds 8 apples and so on up to 5th basket. He now realizes that each basket contains the same number of apples. How many apples were there in the 5th basket in the beginning?

• 8
• 32
• 16
• 24

If 3w = 36 and w - k = 4, then the value of 2k + w is :

• 26
• 32
• 44
• 28

Given besides is the picture of a sheet of the newspaper. Each sheet has 4 pages, the page numbers 8 and 61 of a sheet are shown. How many sheets are there altogether in the newspaper?

• 68

• 17

• 31

• 14

Kisan plants 60 tulip bulbs in his garden. When they flow, he notices the following: (i) Half the tulips are yellow (ii) One third of those which are not yellow are red. (iii) One quarter of those which are neither red nor yellow are pink. (iv) the remainder are white. How many of the tulips are white?

• 10
• 5
• 12
• 15

In a certain year, the month of December has exactly four Tuesdays and hour Fridays. On which day of the week was the New Year celebrated the next year?

• Tuesday
• Saturday
• Monday
• Thursday

A pattern that repeats every six symbols starts as shown besides. What are the 100th and 101st symbols in the pattern?

• 
• 
• 
• 

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through how many degrees?

• 145⁰
• 155⁰
• 152⁰
• 140⁰

If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ?

• 16
• 0.016
• 0.16
• 1.6

Which one of the following is divisible by 6?

• One Million minus One
• One Million minus Two
• One Million minus Six
• One Million minus Four