IMAT 2011 Q36 [Fishing Club]

A fishing club wishes to send out a mailing to its 1000 members. All members receive a magazine (100g). There are 50 committee members who receive minutes (50g). A questionnaire (75g) will be sent to 100 members. No committee members will be sent a questionnaire. The envelope used for all mailings weighs 10g.

The postal rates are:

Up to 120g: 20c

Up to 160g: 30c

Up to 250g: 35c

What is the minimum cost of this mailing?

A. € 67 .00

B. € 215 .00

C. € 220 .00

D. € 230 .00

E. € 350 .00

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?

To start the question, start by dividing up who will get what. There will be three different groups: Magazine only (100g), magazine + minutes (150g), and magazine + questionnaire ($175g) (Note that I have not added the weight of the envelope, this will be done next step). We know that committee members (who receive minutes) cannot receive the questionnaire as well, so no one will have all three items. We now need to find the amount of members in each group, then which postal rate applies to them, and finally the cost of that group’s mailing.

Magazine only

  1. Number of members = 1000 - 50 (committee) - 100 (questionnaire)

= 850

  1. Total weight will be magazine + envelope, therefore 100g + 10g = 110g

This means the rate is up to 120g costing 20c per mailing.

  1. (20c)(850) = 17000c
\frac{17000c}{100c/€}

=€170.00

Magazine + Minutes

  1. Number of members = 50

  2. Total weight will be magazine + minutes + envelope, therefore 100g + 50g + 10g = 160g

This means the rate is up to 160g costing 30c per mailing.

  1. (30c)(50) = 1500c
\frac{1500c}{100c/€}

=€15.00

Magazine + Questionnaire

  1. Number of members = 100

  2. Total weight will be magazine + envelope, therefore 100g + 75g +10g = 185g

This means the rate is up to 250g costing 35c per mailing.

  1. (35c)(100) = 3500c
\frac{3500c}{100c/€}

=€35.00

Final step: Add up the totals

Total cost = €170.00 + €15.00 + €35.00

\fcolorbox{red}{grey!30}{Total cost = $€220.00$, therefore the answer is C.}

Final tips: When doing these calculations, I would recommend practicing multiplication and division, so you are not doubting yourself on exam day. Although 850 times 20 looks easy, it can be tricky. I would use a trick by doing 2 times 850 and then just add an extra 0 on the answer. It may seem trivial but the mind likes to doubt itself under stress.