IMAT 2014 Q12 [Golf Tournament]

Past Papers Solutions Archives
,
1

A golf tournament is played over 10 rounds, on successive Saturdays. The winner of each round scores 3 points and the player finishing second scores 1 point. The tournament is won by the competitor with the most points over the 10 rounds.
Alan Vinci, Barry Durand, Carl Johansson and Daniel and Eric Lim were the participants in this year’s tournament. All five won at least one round, but either Barry, Daniel or Eric finished second on each occasion. The 1­-2 finishing order was different every round, and the Lim brothers didn’t both score points in the same round at any time.

Who won this year’s tournament?

A. Eric Lim
B. Daniel Lim
C. Barry Durand
D. Carl Johansson
E. Alan Vinci

2

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.

Givens:

10 rounds

3 points per win, 1 point for second place

Each win 1 round

Either Barry Daniel or Eric finished second every time

1-2 order was different each time (we cannot have the same combination twice)

Approach: find all possible combination and then determine who has the most points.

What are the possible combinations? You can easily draw a diagram like this, notice that the red circles indicate those who can finish in second In the image there are 10 total lines, which is perfectly all the combinations given in the question.

Imat 2014 q12

Summary:

  1. Alex (1st) + Bary (2nd)

  2. Alex (1st) + Daniel L. (2nd)

  3. Alex (1st) + Eric L. (2nd)

  4. Barry (1st$) + Daniel L. (2nd)

  5. Barry (1st$) + Eric L. (2nd)

  6. Carl (1st) + Bary (2nd)

  7. Carl (1st) + Daniel L. (2nd)

  8. Carl (1st) + Eric L. (2nd)

  9. Daniel L (1st) + Bary (2nd)

  10. Eric L. (1st) + Bary (2nd)

Now all we have to do is count the totals, remembering that 1st place is worth 3 and 2nd place worth 1.

Alan’s total = (3)(3 points) = 9 points

Barry’s total = (2)(3 points) + (4)(1 points)= 10 points

Carl’s total = (3)(3 points) = 9 points

Daniel L.’s total = (1)(3 points) + (3)(1 points) = 6 points

Eric L’s total = (1)(3 points) + (3)(1 points) = 6 points

\fcolorbox{red}{grey!30}{Therefore the answer is C, Barry.}