IMAT 2011 Q18 [Local Supermarkets]

My three local supermarkets all currently have offers on my favourite breakfast cereal as

1 Buy one standard pack get a second half price.
2 Price of a standard pack reduced by 1/3.
3 Normal price of a standard pack, pack contains 25% extra.

Which of the offers are equivalent in terms of price per unit amount of cereal?

A. 1 and 2 only

B. 1 and 3 only

C. 2 and 3 only

D. 1, 2 and 3

E. none

Some Quick Questions to ask yourself when doing this type of problem-solving:

  • What is being asked? Underline the specifics in the question.
  • Analyse the data, is there anything we can eliminate immediately?
  • What information do I need to solve the question? Where can I find it?
  • How can I draw or use the graph to help me?

Approach: We are being asked what is the same price per unit amount of cereal, so we want to take each offer (1, 2, and 3) and then try and find their price per unit.

The best way to do this is to start by assigning easy numbers that you can calculate quickly. Let’s use 1 kg and $1.

In 1, we have 1 for normal price and then 1 bag for half price. So 1kg for $1 or 2kg for $1.5. Therefore the cheapest price is 1kg for $0.75

In 2, it is 1kg for $0.66. This can be calculated by dividing $1 by 3 and then taking this answer away from $1.

3 is a bit trickier because we need to change the kilo amount instead of money. So 1.25kg per $1. This is where some mental math tricks can come into mind, I know that 20% of 1.25 is 0.25, so 1kg for $1-0.20 = 1kg per $0.80.

Now we go back to the question and we can determine that none of the answers are the same.

Therefore E, none, is correct.