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In a multi-voting system, voters can vote for more than one candidate.

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Bunuel
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In a multi-voting system, voters can vote for more than one candidate. [#permalink] New post   11 Feb 2020, 03:57
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61% (01:17) correct 39% (01:26) wrong based on 97 sessions
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In a multi-voting system, voters can vote for more than one candidate. Two candidates A and B are contesting the election. 100 voters voted for A. Fifty out of 250 voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for B?

(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
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C
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Re: In a multi-voting system, voters can vote for more than one candidate. [#permalink] New post   11 Feb 2020, 05:49
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2x2 matrix

---Va---NVa---Total
Vb--50--150---200
NvB--50--0----50
total--100--150--250

IMO C;150


Bunuel wrote:
In a multi-voting system, voters can vote for more than one candidate. Two candidates A and B are contesting the election. 100 voters voted for A. Fifty out of 250 voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for B?

(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
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IanStewart
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Re: In a multi-voting system, voters can vote for more than one candidate. [#permalink] New post   11 Feb 2020, 07:29
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Bunuel wrote:
In a multi-voting system, voters can vote for more than one candidate. Two candidates A and B are contesting the election. 100 voters voted for A. Fifty out of 250 voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for B?



If 100 voted for A, then the rest of the people, 150 people, must have only voted for B (since we know they voted for somebody). That 50 people voted for both candidates is irrelevant to the question.
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In a multi-voting system, voters can vote for more than one candidate. [#permalink] New post   Updated on: 01 Nov 2021, 11:11
IanStewart wrote:
Bunuel wrote:
In a multi-voting system, voters can vote for more than one candidate. Two candidates A and B are contesting the election. 100 voters voted for A. Fifty out of 250 voters voted for both candidates. If each voter voted for at least one of the two candidates, then how many candidates voted only for B?



If 100 voted for A, then the rest of the people, 150 people, must have only voted for B (since we know they voted for somebody). That 50 people voted for both candidates is irrelevant to the question.


the information in the problem is vague, it doesn't state 100 voters voted only for A. it MUST had it mentioned

Originally posted by Limbol on 31 Oct 2021, 04:39.
Last edited by Limbol on 01 Nov 2021, 11:11, edited 1 time in total.
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Re: In a multi-voting system, voters can vote for more than one candidate. [#permalink] New post   31 Oct 2021, 05:13
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Limbol wrote:
the information in the problem is vague, it doesn't state 100 voters voted only for A.


You're right - if the question meant to say that 100 voters voted only for A, the question would need to make that very clear. But that's not what the question means (or that's not what I think it means - I didn't write the question). It means what it says -- that 100 voters voted for A. Some of those 100 voters voted only for A, and some of them voted for both A and B. The remaining 150 voters must have then voted only for B, because we know they voted for at least one of the two candidates, and they didn't vote for A.
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Re: In a multi-voting system, voters can vote for more than one candidate. [#permalink]
31 Oct 2021, 05:13
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