IMAT 2020 Q6 [Washing Powder]

LoCost sells three different types of washing powder: Zoom, Zap and Ownbrand. Zoom is a double concentrate brand needing only half the amount of powder used by the other two brands.

Which one of the boxes of powder below represents best value for money?

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

Many people solving this question may try to find out the price per kilogram, which is effective, however right away I see that option B has a decimal in cents that is difficult to divide by two, so getting its price per kilo won’t be easy mentally. Instead, you can double all the 1kg products in order to get easier numbers to work with at the same weight. We also know that Zoom is twice as powerful, so we either need to double the amount of the others to see how the price compares or we need to half the value of zoom. Again, same situation, doubling the number of others is easier, so we want to find the cost of 4kg of the other brands in order to compare. Why are we doing this? If it is double as efficient, you can half the amount for the same washing, so we want to base it off price per number of loads of washing.

A: Zap
2kg for £2.40
(2kg for £2.40)(2) = 4kg for £4.80

B: Zoom
2kg for £4.95

C: Zoom
1kg for £2.50
(1kg for £2.50)(2) = 2kg for £5.00

D: Own Brand
1kg for £1.25
(1kg for £1.25)(4) = 4kg for £5.00

E: ZAP (I will show in order for completeness but notice that D is the same concentration but a cheaper price, so we can eliminate this by eyeballing)
1kg for £1.30
(1kg for £1.30)(4) = 4kg for £5.20

Now that they are all in comparable quantities, we can see that A shows the best value per money because it is the cheapest option in comparable quantities (meaning cheapest per wash).

\fcolorbox{red}{grey!30}{Therefore the answer is A, ZAP}