## March 2013 Logic & Maths Puzzles

1. Split 45 into four smaller numbers, A, B, C and D so that if you
Subtract two from B
Multiply C by two
Divide D by two
you get the same answer in each case.
Write down the value of A, B, C and D

2. A farmer is asked how many animals he owns.
He replies:
All sheep but three, all goats but four and all horses but five
How many animals does he own?

3. The street number of my friend’s house is the reverse of my street number.
The difference between our house numbers ends in 2.
What are the lowest possible numbers of our houses?

4. Bert scores an average of 73% over each of his first three tests. What will he need to score on his fourth and final test to bump his average up to 80%?

5.
1 + 23 + 4 + 5 + 67 =100
is one way of inserting plus signs into 1234567 so that the total is 100.
Find another way.

6. A house painter was asked to mix 6 litres of gray in the ratio of two parts white to one part black.
By mistake, he mixes 4 litres of black with two litres of white.
He decides to pour away some of the incorrect mixture and to correct the remainder by adding sufficient volume of white paint to achieve 6 litres of gray paint in a 2:1 white:black ratio.
What is the minimum volume he needs to pour away?

7. A proper fraction is a fraction written as a numerator over a denominator with a value of more than 0 but less than 1.
What is the highest value proper fraction (in other words that has a value
closest to 1) you can write using the digits 1, 2, 3, 4, 5 and 6 once each?
For example, 354/612 has a value of more than a half, but the correct answer is bigger than that.
8. Using each of the digits 1 to 6 once only, write down two three-digit numbers
and multiply them together.
For example, 654 X 231 = 151,074 but that isn’t the biggest number you can make following these rules:
What is?

9. Tuesday’s high temperature was 4 degrees Celsius warmer than that of Monday’s.
Wednesday’s high temperature was 6 degrees Celsius cooler than that of Monday’s.
If Tuesday’s high temperature was 22 degrees Celsius, what was Wednesday’s high temperature?

10. A bat and ball purchased together cost \$1.10
If the bat costs \$1 more than the ball then what does the ball cost?

SOLUTIONS