5A 5B 5C 5D 5E Question Olympiad

Question

5A

Charlotte buys two biscuits and a carton of milk for $5.00.

Oliver buys three biscuits and a carton of milk for $6.50.

How much more does a carton of milk cost than a single biscuit?

5B

27 ÷ N has a remainder of 3.

How different positive integers could N be?

5C

Some identical cubes are arranged in a pyramid-like form with 5 layers. Starting from the bottom layer, the number of cubes in the layers are 5 x 5, then 4 x 4, then 3 x 3, then 2 x 2, then 1 x 1. The whole exterior of the pyramid is painted including the bottom. How many of the cubes will have none of their faces painted?

5D

Chloe notices that 91 = 100 - 9 = (10 + 3) x (10 - 3) = 13 x 7.

Since 7 and 13 are primes, 91 has two prime factors.

Mia notices that 391 = 400 - 9 = (20 + 3) x (20 - 3) = 23 x 17.

Since 17 and 23 are primes, 391 has two prime factors.

Using the same method, Ruby finds prime factors of 1591.

Find the sum of Ruby's prime factors.

5E

There are 5 different coloured cups in a row.

1. The green cup is to the left of the red cup (but not necessarily next to it).
2. The yellow cup is to the left of the purple cup (but not necessarily next to it).
3. The blue cups is on one end of the row of cups.

For all these 3 statements to be true, how many different ways could these 5 cups be arranged?

Answer 1

1 biscuit cost $1.50

1 milk carton costs $2

2(1.5) + 2= 5

3(1.5) +2 = 6.5

the milk is 50 cents more

N= 24 is the only positive value that divides 27 with remainder of 3