IMAT 2015 Q2 [Invitation Cards]

Tom is having a celebration and needs to send out 50 invitation cards. The cards must be at least 6 cm wide and at least 8 cm high and Tom wants to put a photo on the card. Each type of card has a standard version and a deluxe version. The prices (per card) that have been quoted to Tom are shown in the table below:

image

Tom wants to buy the cheapest type of card possible but is willing to pay for the deluxe version instead of the standard.

What is the total extra that Tom would have to pay to buy the deluxe cards?

A. €30.00
B. €20.00
C. €25.00
D. €22.50
E. €27.50

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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.

Approach: Eliminate all the options that do not meet Tom’s criteria. Next, take the cheapest standard cards that meet this criteria and price out the cost of 50 of them. Then do the same with the cheapest deluxe cards that meet the criteria. Finally, take the difference between the two.

Criteria:

Card Dimensions: Width ≥6cm and Height ≥8cm

Must have photo

Personal Greeting? Non specified so it does not matter if it does or not.

All card types in the table are at least 6cm, but card rows 1 and 4 are less than 8cm.

Then we can eliminate the rows that do not have a picture, which is only row 2.

So the remaining options are rows 3, 5, 6, 7

The row with the cheapest price for the standard card (out of the ones that meet the criteria) is row 5, costing €1.50.

The row with the cheapest deluxe card price (that meets the criteria) is also row 5, costing €1.95.

Now, all we have to do is multiply them each by 50 (one for each guest) and find the difference.

Cost of cheap cards = (50)(€1.50)

= €$75.00$

Math trick:

(1.00)(50) = 50

(0.50)(50)=25

Cost of cheap cards = (50)(€1.95)

= €50 + €47.50

=€97.50

Math trick:

(1.00)(50) = 50

[(0.95)(100)]/2 = 95/2 =47.50

Finally, take the difference between the two:

Extra cost of deluxe for Tom = $€97.50 - €75.00

= €22.50

\fcolorbox{red}{grey!30}{Therefore D is the correct answer.}