Imat 2012 Q32 math/logic

The answer is A. But i picked rachel because the gap in degrees between her and the rest was too big in my opinion.
the table below shows the number of people who voted for each candidate in the recent school election:

image

When drawing a pie chart of the results one of the numbers above was not read correctly (the other four were correct). The angles were calculated as 113.4 degrees, 90 degrees, 75.6 degrees, 56.7 degrees, and 24.3 degrees.

Whose score was copied incorrectly when the pie chart was constructed?

A. Kevin
B. Peter
C. Rachel
D. Alison
E. Harold

Hi! This was a tough one but @Juliette solved this for us!!

First, what score is incorrect?
P has the highest votes, so i’m assuming P = 113° is correct.
No one has less than half of P’s votes, so we can’t have an angle less than 56,7°.
The only angle in the pie chart less than 56,7° is 24,3°.
So 24,3° was copied incorrectly.

Now who has what angle?
P = 2 x R so R = 56,7°.
P = 1,5 x A so A = 75,6°
We have too angles left over, K < H and H > A.
So H has a bigger angle than A, meaning H = 90° and we are left with K = 24,3°
So K was copied incorrectly.

3 Likes

Hi!
Thanks for the solution, makes sense!