simple fraction q, but i got it wrong

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simple fraction q, but i got it wrong

by tj123 » Mon Jun 22, 2009 10:27 pm

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At least 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote against the resoltion and still have it pass?

A) 19
B) 17
c) 16
D) 14
e) 13

OA e

[spoiler] I chose B because 2/3 of 40 is 26, which means 14 is the max that can vote against a resolution and still have it pass. why is my methodology wrong[/spoiler]

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by pops » Mon Jun 22, 2009 10:38 pm
No,
If 14 votes against the resolution then it wont pass since:
26/40 = 0.65 and required is 2/3 = 0.66

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Re: simple fraction q, but i got it wrong

by BlindVision » Tue Jun 23, 2009 12:54 am
tj123 wrote:At least 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote against the resoltion and still have it pass?

A) 19
B) 17
c) 16
D) 14
e) 13

OA e

[spoiler] I chose B because 2/3 of 40 is 26, which means 14 is the max that can vote against a resolution and still have it pass. why is my methodology wrong[/spoiler]
If 2/3 = for resolution to pass then 1/3 = resolution to not pass.

The question is asking what is the most votes of "resolution to not pass" and "still have it pass"

40(1/3) = 13.3, rounded to 13

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by rah_pandey » Tue Jun 23, 2009 3:45 am
I think the confusion is with decimals as 80/3 is not integer. So the thumb rule for passing a resolution
an integer no of votes should be in favour
if by solving we get a fraction than it needs to rounded off to next HIGHER integer even if fraction part is less than 0.5

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by ssmiles08 » Tue Jun 23, 2009 5:13 am
Alternatively, you can find the minimum to pass to find the maximum that can vote no.

for the bill to pass at least 2/3 ~ 2/3(40) = 26.667 ~ 27 (b/c 26 votes will still cause a bill to fail)

so the rest of the votes can be no 40-27 = 13. (E)

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by tj123 » Tue Jun 23, 2009 9:49 am
thanks i should have rounded up.
that was my mistake
thanks

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by [email protected] » Thu Mar 15, 2018 7:14 pm
Hi All,

In these types of questions, it's important to remember that you can't have a 'fraction of a person.' Thus, you have to pay attention to the question that is ASKED and think in terms of 'whole persons.'

Here, we're told that AT LEAST 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. Since 2/3 of 40 is 26.666666, but we can't have 26.666666 people, we have to round UP to 27. In contrast, 26 people would NOT be enough, since 26/40 = 13/20 = 65% (and not the 66 2/3% minimum that a resolution needs to be passed).

Knowing that it would take AT LEAST 27 people to pass a resolution, the GREATEST number who could vote AGAINST the resolution in this case would be 40-27 = 13.

Final Answer: E

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by Scott@TargetTestPrep » Mon Mar 19, 2018 3:36 pm
tj123 wrote:At least 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote against the resoltion and still have it pass?

A) 19
B) 17
c) 16
D) 14
e) 13
We are given that at least 2/3 of the members must vote IN FAVOR of a resolution in order for it to pass; however, we need to determine the greatest number of members who could vote AGAINST the resolution and still cause its passage. Remember, in a vote there are only two options, voting in FAVOR and voting AGAINST. Thus, we know the following:

2/3 of total voters need to vote in FAVOR for it to pass; this means that 1/3 of total voters can vote AGAINST for it to pass.

To finish the problem, we can set up the following equation:

1/3 x 40 = total votes AGAINST to have resolution pass

1/3 x 40 = 40/3 = 13 1/3 voters

Since we need the resolution TO PASS, we must round this number down to 13. Thus, 13 voters can vote against the resolution and still have it pass.

Alternate Solution:

Notice that 2/3 x 40 = 80/3 = 26 2/3 and we have to round this up to 27 because 26 people out of 40 does not satisfy the requirement of "at least 2/3 of the voters". . Therefore, we need at least 27 voters to vote IN FAVOR of the resolution to pass it. This means that we can have at most 40 - 27 = 13 individuals voting AGAINST it, and still it will pass. Therefore, the maximum number of voters who can vote against it and still have it pass is 13.

Answer: E

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by BTGmoderatorRO » Sun Mar 25, 2018 7:07 am
At least 2/3of the 40 members.
To vote for $$\frac{2}{3}\cdot40=26.7$$
To vote against = $$\left(1-\frac{2}{3}\right)\cdot40=\left(\frac{\left(3-2\right)}{3}\cdot40\right)=13.3$$
To the nearest whole number, we have 13people (E)