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M00-04

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New post 16 Sep 2014, 00:14
1
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

100% (01:08) correct 0% (00:00) wrong based on 32 sessions

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60 percent of the people surveyed said that they would vote for Stewart. Of those who said they would vote for Stewart, 90 percent actually voted for him, and of those who did not say that they would vote for Stewart, 5 percent actually voted for him. What percent of the group surveyed voted for Stewart?

A. 30%
B. 40%
C. 50%
D. 56%
E. 64%

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New post 16 Sep 2014, 00:14
Official Solution:

60 percent of the people surveyed said that they would vote for Stewart. Of those who said they would vote for Stewart, 90 percent actually voted for him, and of those who did not say that they would vote for Stewart, 5 percent actually voted for him. What percent of the group surveyed voted for Stewart?

A. 30%
B. 40%
C. 50%
D. 56%
E. 64%


Let \(X\) be the total number of polled people.
  • \(0.6X\) -- say that they will vote for Stewart
  • \(0.9*0.6X=0.54\) -- actually voted
  • \(0.4X\) -- will not vote for Stewart
  • \(0.05*0.4X=0.02X\) -- nevertheless, voted for him

So, \(0.54X+0.02X=0.56X\) or 56%


Answer: D
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New post 17 Feb 2017, 22:31
Let X, total # of people=100.. simplest way if you want to avoid the decimals with variable x
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New post 19 Apr 2017, 06:47
yeah right so much easier with real numbers.
Although x is 100 :D
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New post 04 Oct 2018, 12:33
I got this wrong on the test but I used the following method while reviewing it and it went much faster than the time I took to solve this on the test.
I started with plugging x=100.
60% surveyed = 60
Out of the 60, 90 actually voted for him = (90/100) * 60 = 54
At this point, I reviewed the answer choices and saw that it can't be E. I then quickly read through the rest of the QS and guessed that it has to be slightly higher than 54.
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M00-04  [#permalink]

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New post 10 Feb 2019, 12:10
I picked numbers in this problem.

I said that the people who vote are 100.
Then 60 said that would vote for Stewart
Then 9/10*60= 54. 54 is the number of people who really voted for him.

From the 40 who said they were not going to vote him, 5% voted for him. Then 5/100=1/20 --> 1/20 * 40= 2.

54+2=56. 56 is the number of people who really voted for him.
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M00-04   [#permalink] 10 Feb 2019, 12:10
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