CSAT Solved Papers/ 2022/Q64

2022 CSAT — Q64

Quant Arithmetic & numeracy 2.5 marks Medium

Two candidates $X$ and $Y$ contested an election. $80\%$ of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. $X$ got $56\%$ of the votes cast and won by $1440$ votes. What is the total number of voters in the voters list?

A 15000 Answer
B 12000
C 9600
D 5000

Worked rationale

Let the voters list have $V$ people. Votes cast $= 0.8V$ . With only $X$ and $Y$ , $X$ got $56\%$ and $Y$ got $44\%$ of the cast votes, so the winning margin is

\text{margin} = (56\% - 44\%)\ \text{of cast} = 12\% \times 0.8V = 0.096V.

Set this equal to $1440$ :

0.096V = 1440 \;\Rightarrow\; V = \frac{1440}{0.096} = 15000.

Answer: (a) 15000.

Why the other options miss

B

percentage on the wrong base: takes $12\%$ of the voters list directly ( $0.12V = 1440$ ), forgetting that only $80\%$ voted.
C

answers the wrong quantity: computes votes cast ( $0.8 \times 12000$ ) instead of the list, mixing the cast figure with the total.
D

an arithmetic slip: divides by a wrong margin (e.g. $0.288$ ) or mis-stacks the percentages.

Specialist insight

The margin is a percentage of a percentage: $12\%$ of the $80\%$ who voted, i.e. $0.096$ of the list. The dominant trap is applying $12\%$ straight to $V$ (giving $12000$ ). Always track which base each percentage sits on — turnout first, then vote-share — and the back-calculation $1440 / 0.096 = 15000$ falls out.

The trap, in one line

Margin $= 12\%$ of cast $= 0.096V = 1440 \Rightarrow V = 15000$ (not $12\%$ of $V$ ) $=$ (a).

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