2/5th of the voters promise to vote for A and the rest promised to vot

Question

2/5th of the voters promise to vote for A and the rest promised to vote for B. Of these, on the last day 15% of the voters went back of their promise to vote for A and 25% of voters went back of their promise to vote for B, and A lost by 200 votes. Then, the total number of voters is:

A. 10000
B. 11000
C. 9000
D. 9500
E. 12000

A. 10000
B. 11000
C. 9000
D. 9500
E. 12000

CrackverbalGMAT · Answer

Let the total number of voters = x

Voters who promised A their votes = 2/5 of x = 0.4x. Voters who promised B = x - 0.4x = 0.6x

Backing from the promise means that those who promised to vote for A, voted for B and vice versa.

15% went back on their promise to A, i.e 0.15 * 0.4x = 0.06x (These went to B)

25% went back on their promise to B, i.e 0.25 * 0.6x = 0.15x (These went to A)

Number of votes received by A = 0.4x - 0.06x + 0.15x = 0.49x

Number of votes received by B = 0.6x - 0.15x + 0.06x = 0.51x

A lost by 200 votes, i.e 0.51x - 0.49x = 200

0.02x = 200

x = 200 / 0.02 = (200 * 100) / 2

x = 10000

Option A

Arun Kumar

Abhishek009 · Answer

Let total voters be 400

160 voters promised to vote for A & 240 voters promised to vote for B

Votes casted in favour of A is 160 - 24 + 60 = 196
Votes casted in favour of B is 240 + 24 - 60 = 204

Difference of votes is 204 - 196 = 8

So, Total voters is  \frac{200}{8}*400 = 10000 , Answer must be (A)

KarishmaB · Answer

2/5th voters promised to vote for A and 3/5th for B.

So '85% of the 2/5th voters + 25% of the 3/5th voters' voted for A
and '75% of the 3/5th voters + 15% of 2/5th voters' voted for B

(\frac{75}{100} * \frac{3}{5} + \frac{15}{100} * \frac{2}{5})* Total = (\frac{85}{100} * \frac{2}{5} + \frac{25}{100} * \frac{3}{5} ) * Total + 200

\frac{2}{100} * Total = 200

Total = 10,000

Answer (A)

CountingBack · Answer

This is a bad question ,because it never clarifies whether "going back on the promise " means not voting at all or voting for the opposite party..

Ezzy · Answer

It says 15% of the voters. So shouldn't it be 15% of x? Why is it 15% of 2x/5?

KarishmaB · Answer

Because 15% of those who promised to vote for A did not vote for A. 
Hence 15% of 2x/5 went back on their promise to vote for A. 
2x/5 is the number of people who promised to vote for A in the first place.

BraydinWalters · Answer

Identify the steps:

Step 1: Identify the original promised voters per participant.
Step 2: Subtract those who went back on their word.
Step 3: Add the subtracted voters to the other candidate.
Step 4: Determine total voters.

Let x represent the total number of voters.

Step 1 
Voters for A: 2/5x
Voters for B: 3/5x

Step 2 
15% or 0.15 or 3/20 of voters for A went back on their word.
2/5 * 3/20 = 6/100 = 3/50

25% or 0.25 or 1/4 voters for B went back on their word.
3/5 * 1/4 = 3/20

Step 3 
Now subtract the fraction of voters from each and add them to the other candidate:
Candidate A: 2/5 - 3/50 + 3/20 = 49/100
Candidate B: 3/5 - 3/20 + 3/50 = 51/100

HINT: You only have to find one value because the total voters have to add up to 100%.

We now have our formula:

Step 4 
51/100x - 49/100x = 200
2/100x = 200
x = 10000
A

2/5th of the voters promise to vote for A and the rest promised to vot

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GMAT Problem Solving (PS) Questions

2/5th of the voters promise to vote for A and the rest promised to vot

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards