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Suppose that in an election voter preference is sharply divided along

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gmat1393
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Suppose that in an election voter preference is sharply divided along [#permalink] New post   29 Jan 2020, 06:50
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Suppose that in an election voter preference is sharply divided along gender lines. 40% of women will vote for candidate A, the rest will vote for candidate B. 70 % of men will vote for candidate A, the rest for candidate B which of the following represents the lowest percentage of voters that must be women on election day in order that candidate B wins the election.

A. 56%
B. 61%
C. 65%
D. 67%
E. 70%
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D
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IanStewart
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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   29 Jan 2020, 08:23
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It's just a weighted average problem, and if you know alligation (if you don't, this explanation might not make much sense) the answer is immediately 2/3: we know 40% of women and 70% of men will vote for A, and we want A to get less than 50% of the vote, so we want the overall vote total to be more than "twice as close" to the women's percentage than to the men's, and we thus need more than twice as many women as men. So the right answer is just slightly greater than 2/3, so is infinitesimally greater than 66 2/3%, which isn't among the answer choices.

If a real GMAT question asks for an exact answer, that exact answer will always be one of the choices. This question does ask for an exact answer, but it means to ask for an approximation. What is the source?
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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   29 Jan 2020, 10:37
IanStewart wrote:
It's just a weighted average problem, and if you know alligation (if you don't, this explanation might not make much sense) the answer is immediately 2/3: we know 40% of women and 70% of men will vote for A, and we want A to get less than 50% of the vote, so we want the overall vote total to be more than "twice as close" to the women's percentage than to the men's, and we thus need more than twice as many women as men. So the right answer is just slightly greater than 2/3, so is infinitesimally greater than 66 2/3%, which isn't among the answer choices.

If a real GMAT question asks for an exact answer, that exact answer will always be one of the choices. This question does ask for an exact answer, but it means to ask for an approximation. What is the source?


It's from an unofficial source
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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   29 Jan 2020, 22:45
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Explanation: Let say Women Voters = F
Male Voters = M
40% of women will vote for candidate A
=(40/100)F  = 0.4F
70 % of men will vote for candidate A
= (70/100)M = 0.7M
Candidate A Votes   = 0.4 F + 0.7M
Candidate B Votes = M + F - (0.4F + 0.7M) = 0.6F + 0.3M
0.6F + 0.3M > 0.4 F + 0.7M (As Given)
=0.2F > 0.4M
=F > 2M
Total M + F
Lowest percentage of voters that must be women on election day in order that candidate B wins the election= 100 * 2M/(M + 2M)
= 66.67 %
66.67 % of Voters Must be Women on  election day in order that candidate B wins the election.

IMO-D
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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   02 Feb 2020, 12:08
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gmat1393 wrote:
Suppose that in an election voter preference is sharply divided along gender lines. 40% of women will vote for candidate A, the rest will vote for candidate B. 70 % of men will vote for candidate A, the rest for candidate B which of the following represents the lowest percentage of voters that must be women on election day in order that candidate B wins the election.

A. 56%
B. 61%
C. 65%
D. 67%
E. 70%


We can let the total number of voters = 100, and n = the number of women. Since, in order for candidate B to win the election, he or she must get more than 50 votes, we can create the inequality:

0.6n + 0.3(100 - n) > 50

0.6n + 30 - 0.3n > 50

0.3n > 20

n > 20/0.3 = 200/3 = 66.67

Therefore, we need to have at least 67 women, or 67% of the voters, to be women.

Answer: D

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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   18 May 2021, 04:15
gmat1393 Why have you taken (100 - n)? Didn't understand where did this come from. Could you please elaborate the whole equation?
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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   18 May 2021, 05:52
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AbhaGanu wrote:
gmat1393 Why have you taken (100 - n)? Didn't understand where did this come from. Could you please elaborate the whole equation?




Hey, if the assumption is total number of women =n
then the number of men should be 100-n right? since we are considering everything in one variable i,e n terms of women we are plugging in 100-n for men.

Hope this resolves your doubt.
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Re: Suppose that in an election voter preference is sharply divided along [#permalink] New post   30 Mar 2024, 06:32
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Re: Suppose that in an election voter preference is sharply divided along [#permalink]
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