IMAT 2018 Q1 [Parliament]

Alpha, Beta, and Gamma are the three political parties in the Parliament.
There are 360 seats in the Parliament. Before last week’s General Election, each party held 120 seats.
In last week’s election:
There was no change in 216 seats.

Alpha gained 15 seats from Beta and 23 seats from Gamma.

Beta gained 31 seats from Alpha and 41 seats from Gamma.

Gamma gained 24 seats from Alpha and 10 seats from Beta.

Which pie chart, suitably labelled, shows the current state of the parties in the Parliament?

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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.

For the format of this question, we need to analyse them one by one, taking what is being added and subtracting what is being taken:

Let A=Alpha, let B=Beta, and G=Gamma

Alpha:
120(A) + 15(B) + 23(G) - 31(B) - 24(G) = 103

Beta
120(B) + 31(A) + 41(G) - 15(A) - 10(G) =167

Gamma
120(G) + 24(A) + 10(B) - 23(A) - 41(G) = 90

With this info, we can easily solve it. Gamma has 90 votes, which means it will be one-quarter of our pie (that has 360 votes). This allows us to eliminate A and D. Next up is Beta, it has less than half but more than a third of the votes. Using this we can eliminate A, B, and C with certainty. The only one that fits all the criteria is E.

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