IMAT 2017 Q1 [Chocolate Tins]

I have a tin of chocolates to share with some friends. In the tin are four types of chocolate – one type in red wrappers, one type in blue, one type in green and one type in yellow, with equal numbers of each.

The tin is passed around in turn from friend to friend. When the tin gets to them:

• John always takes three red chocolates.
• Peter always takes one of each colour.
• Jane always takes one yellow chocolate.
• I always take two green chocolates.

After six passings around of the tin, half of the chocolates remaining in the tin are blue.

How many chocolates were there in the tin when it was full?

A. 48
B. 24
C. 72
D. 96
E. 60

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.

This is an important question for analysis because it has appeared over the history of IMAT more than once. Small details change, but the main ideas are the same. It is important you recognize patterns and repetition, the exam is best succeeded studying high-yield material, so trust your review and focus on what is the most frequently asked.

The best approach is to calculate how many of each chocolate is taken per turn, and we will continue from there.

Red
John takes 3 each turn, Peter takes 1
After 6 turns: (3+1) (6) = 24

Blue
Peter takes 1
(1) (6) = 6

Green
I take 2, Peter takes 1
(2+1) (6) = 18

Yellow
Jane takes 1, Peter takes 1
(1+1) (6) = 12

Now we can take the rest of the info. All colours are equal, and half the ones left after 6 turns are blue.

Looking at our answer options, we can easily eliminate all of them but one. Why? Because we know that Red = Blue = Green = Yellow

Red is at least 24 chocolates, so there must be at least 24 chocolates each. (4)(24) = 96.

This is a very important observation. We completely skipped the fact that ‘After six passings around of the tin, half of the chocolates remaining in the tin are blue’. This is an important statement but it complicates things and we could already conclude that the answer was 96 because nothing else was suitable.

For the sake of completion and to convince you we can skip this step:

If half the chocolates left are blue, and we are assuming there are 24 of each, it means that 24-6 blue are left, =18.

Yellow left = 24 - 12
Green left = 24 - 18 = 6
Red left = 24 - 24 = 0

Yellow + Green = Blue

So half the remaining chocolates were blue.

\fcolorbox{red}{grey!30}{Therefore the answer is D, $96$.}