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which is the right answer ?

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which is the right answer ?

by Uva@90 » Tue Jul 16, 2013 2:35 am
In an election how many votes are cast.
1. the winning candidate gets 54% of the total votes
2. the winning candidate wins by 800

As per the solution asnwer is E

But my solution is C

Please suggest me which is the right one.

Thanks in advance.
Regards,
Uva.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Jul 16, 2013 6:20 am
Uva@90 wrote:In an election how many votes are cast.
1. the winning candidate gets 54% of the total votes
2. the winning candidate wins by 800

As per the solution asnwer is E

But my solution is C

Please suggest me which is the right one.

Thanks in advance.
Regards,
Uva.
The answer depends on how many candidates are running in the election. If we assume that there are only 2 candidates, then the correct answer is C. If there are more candidates, then the correct answer is E

To demonstrate this, let's examine two conflicting cases that meet the criteria in statements 1 and 2
Case a:
Candidate A: 2700 votes
Candidate B: 1900 votes
Candidate C: 400 votes
TOTAL VOTES = 5000
Notice that Candidate A wins by 800 votes AND he/she gets 54% of the total votes

Case b:
Candidate A: 3240 votes
Candidate B: 2440 votes
Candidate C: 320 votes
TOTAL VOTES = 6000
Notice that Candidate A wins by 800 votes AND he/she gets 54% of the total votes

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Tue Jul 16, 2013 6:24 am, edited 1 time in total.
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by jitsy » Tue Jul 16, 2013 6:23 am
Uva@90 wrote:In an election how many votes are cast.
1. the winning candidate gets 54% of the total votes
2. the winning candidate wins by 800

As per the solution asnwer is E

But my solution is C

Please suggest me which is the right one.

Thanks in advance.
Regards,
Uva.


Hi Uva@90

I hope you did not read the second statement as saying 'the winning candidate got 800 votes' which is different. If you did not, please continue to read below.

The first statement only says 'the winning candidate gets 54% of the total votes'. Since you arrived at C as the answer, I assume you do understand that this statement alone is not sufficient.

The second statement says 'the winning candidate wins by 800'. You also do understand that this statement alone is not sufficient.

Now lets try to evaluate both statements together. There are two things here we don't know.
a) The winning candidate could have got say, 1000 votes and the second candidate in that case would have got 200 (1000-800). In another case the winning candidate could have got 900 votes and the second candidate in that case would have got 100 votes. So the point is we do not know what case to combine data from statement 1 with. We do not have ONE answer here.
b) Just for your knowledge - even if the second statement said, 'the winning candidate wins by 800 and the second candidate won 100' statement 2 would not alone have been sufficient since we could not have assumed that there were only 2 candidates. There could have been a third candidate who won 50 votes. However we would have been able to combine this statement with statement 1 and arrive at C as the answer.

I am not an expert, so experts - please let us know if you have any additional inputs or if this is not correct.
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by Brent@GMATPrepNow » Tue Jul 16, 2013 6:31 am
Uva@90 wrote:In an election how many votes are cast.
1. the winning candidate gets 54% of the total votes
2. the winning candidate wins by 800
Now let's assume that there are only 2 candidates.

Target question: How many votes are cast?

Let W = # of votes cast for the winner
Let L = # of votes cast for the loser

Rephrased target question: What is the value of W + L?

Statement 1: The winning candidate gets 54% of the total votes
So, W = 54% of total votes cast
Since W + L = total votes cast, we can write the equation:
W = 0.54(W + L)
Does this provide enough information to find the value of W + L?
No.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The winning candidate wins by 800
In other words, W = L + 800
Does this provide enough information to find the value of W + L?
No.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1, we know that W = 0.54(W + L)
From statement 2, we know that W = L + 800
Since we have two different linear equations, we could solve this system for W and L, which means we definitely could find the value of W + L
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by Uva@90 » Tue Jul 16, 2013 8:35 am
Brent@GMATPrepNow wrote:
Uva@90 wrote:In an election how many votes are cast.
1. the winning candidate gets 54% of the total votes
2. the winning candidate wins by 800

As per the solution asnwer is E

But my solution is C

Please suggest me which is the right one.

Thanks in advance.
Regards,
Uva.
The answer depends on how many candidates are running in the election. If we assume that there are only 2 candidates, then the correct answer is C. If there are more candidates, then the correct answer is E

Brent,
Will these kind of conflict question appears on Actual GMAT ?
If Yes, to which answer should I go for ?

Regards,
Uva.
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by jitsy » Tue Jul 16, 2013 8:48 am
I know you addressed the question to Brent - but would just like to tell you that I have come across questions like these (votes and candidates) in the past and what the test makers are almost always testing here is if the person falls for the trap - which is assuming that there are only 2 candidates. So never assume its 2 unless the question in some way communicates that.
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by Brent@GMATPrepNow » Tue Jul 16, 2013 8:48 am
Uva@90 wrote: Brent,
Will these kind of conflict question appears on Actual GMAT ?
If Yes, to which answer should I go for ?

Regards,
Uva.
Good question. Some have argued that the question is ambiguous. I'm not entirely sure that I agree.
A good rule to follow is: If a question does not include restrictions on certain values (e.g., the number of candidates), then don't assume that restrictions exist.

The GMAT has lots of questions that trick people into making assumptions about certain values (as well as failing to make certain assumptions). We have a free video on this: https://gmatprepnow.com/module/gmat-data ... cy?id=1105

Cheers,
Brent
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by Uva@90 » Tue Jul 16, 2013 7:14 pm
Hi Jitsy/Brent,

Thanks a lot for helping me.

Regards,
Uva.
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