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# Of the 9,000 people who voted in a recent election, how many

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Of the 9,000 people who voted in a recent election, how many [#permalink]

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25 Jul 2011, 12:41
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Of the 9,000 people who voted in a recent election, how many women voted for candidate X?

1) The percentage of women voting for candidate X was twice the percentage of women voting against candidate X.
2) 3000 men voted for candidate X.
[Reveal] Spoiler: OA

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Re: Women votes for Candidate X [#permalink]

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25 Jul 2011, 23:15
Statement (1) is not enough because from the percentage of women who voted for candidate X being twice that of men who voted for candidate X, we cannot find the number of women who voted for candidate X.
For example, it is possible that from the 9000 people who voted, 5000 were women and 4000 were women. If 20% of the voting women voted for candidate X, and only 10% of the men did, candidate X would be 1,400 votes. However, if 40% women voted for candidate X and 20% men did, then candidate X would get 2,800 votes. In both cases the number of women voting for candidate X is different and yet statement (1) is satisfied.
Therefore statement (1) is insufficient alone.

Using statement (2), we know the number of men who voted for candidate X. However, this does not give us the number of men who voted, nor does it give us either the number of women who voted or the number of women who voted for candidate X.
Therefore statement (2) alone is also insufficient.

Now combine statement (1) and statement (2):
We now know the number of men who voted for candidate X but we still do not know the total number of men who voted. We need to know this because without knowing this, we cannot calculate the total number of women who voted. And without knowing the number of total women who voted, we cannot find the percentage of women who voted for candidate X to arrive at the number of women who voted for candidate X.

Therefore statement (1) and (2) together are also insufficient. The answer is (E).
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Re: Women votes for Candidate X [#permalink]

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26 Jul 2011, 08:37
1) The percentage of women voting for candidate X was twice the percentage of women voting against candidate X.

This choice does not tell how what is total number of women out of 9000 candidates.
So insufficient.

2) 3000 men voted for candidate X.
Using this choice it is not possible to calculate how many women contested among 9000 candidates neither does it tell how many women voted for or against candidate X.

Combining both the options:
from 1 we know % of women voted for candidate X is twice %age of women voted against X
and from 2 we know men voted for candidate X, but we don't know number of men voting against X. So we cannot find the total number of women contesting elections.
So insufficient.

So E
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Re: Of the 9,000 people who voted in a recent election, how many [#permalink]

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09 Oct 2017, 06:00
Suppose the question was the percentage of men voting for candidate X is the same as the percentage of women voting for candidate X ....then we'd be able to solve the question as C correct???

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Re: Of the 9,000 people who voted in a recent election, how many [#permalink]

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10 Oct 2017, 10:02
fluke wrote:
Of the 9,000 people who voted in a recent election, how many women voted for candidate X?

1) The percentage of women voting for candidate X was twice the percentage of women voting against candidate X.
2) 3000 men voted for candidate X.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

..........| Men | Women
------------------------------
.... for X | a | b
------------------------------
against X | c | d

=> Q: b = ?

a + b + c + d = 9000

Since we have 4 variables and 1 equation, E could be the answer most likely.

1) & 2)
From the condition 1), we have b = 2d.
From the condition 2), we have a = 3000.

Since we have only 2 equations b = 2d and a = 3000, we can't figure out b and solve this question.

Therefore, the answer is E as expected.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
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Re: Of the 9,000 people who voted in a recent election, how many   [#permalink] 10 Oct 2017, 10:02
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# Of the 9,000 people who voted in a recent election, how many

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