Maths Olympiads 2010 Questions and Solutions

1. What is the value of the following?
(8 x 4)+(8 x 3)+(8 x 2)+(8 x 1)

Solutions :
Method 1
You just need to know your timestable well to get this questions correct.
32+24+16+8=80

Method 2
Understand that there is a Distributive Law which allows you to add first before multiplying, that is
(8 x 4)+(8 x 3)+(8 x 2)+(8 x 1) = 8 x (4+3+2+1) = 8 x 10 = 80

Find out more about the other laws from the weblink below
http://www.mathsisfun.com/associative-commutative-distributive.html

Q2. A bag contains 18 jelly beans, 4 are red, 6 are white and 8 are blue. Amanda takes them out one at a time without looking. What is the fewest jelly beans she must take out to be certain that at least 2 of the jelly beans she takes out are blue?

Method : Consider the worst case scenario
4 red + 6 white + 2 blue = 12 jelly beans

Q3. A prime number is a counting number with exactly two factors, the number itself and the number 1. In the sequence 2, 5, 11, 23, ... each number is obtained by doubling the previous number and adding 1.What is the first number in the sequence that is not a prime number?

Solution :
You should know about prime numbers before you can attempt this question. Using listing method and checking each number. Noticed that the first four numbers are all prime numbers.
2, 5, 11, 23,...
Continue to list...
47, 95...
95 is not a prime number because it is a multiple of 5.

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