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Among a group of 2,500 people, 35 percent invest in [#permalink]
14 Jun 2012, 01:49

Expert's post

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Difficulty:

25% (medium)

Question Stats:

73% (02:30) correct
27% (02:00) wrong based on 354 sessions

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

(A) 9/50 (B) 7/25 (C) 7/20 (D) 21/50 (E) 27/50

Diagnostic Test Question: 4 Page: 20 Difficulty: 650

Re: Among a group of 2,500 people, 35 percent invest in [#permalink]
14 Jun 2012, 01:49

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Expert's post

SOLUTION

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

(A) 9/50 (B) 7/25 (C) 7/20 (D) 21/50 (E) 27/50

Given: 0.35*2,500=875 invest in municipal bonds; 0.07*2,500=175 invest in in both municipal bonds and oil stocks;

Therefore 875-175=700 invest in municipal bonds but NOT in in oil stocks. (Or directly: 35%-7%=28% of 2,500, which is 700, invest in municipal bonds but NOT in in oil stocks).

Re: Among a group of 2,500 people, 35 percent invest in [#permalink]
14 Jun 2012, 05:09

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Quote:

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

(A) 9/50 (B) 7/25 (C) 7/20 (D) 21/50 (E) 27/50

Hi,

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks.

As per the attached venn diagram, we have to find the number of people in shaded portion. =35%-7%=28%

Thus, probability = 0.28 = 7/25

(2,500 people, 18 percent invest in oil stocks is not required.)

Re: Among a group of 2,500 people, 35 percent invest in [#permalink]
14 Jun 2012, 05:50

People with Municipal Bond but not with Oil Stock = People with Municipal Bond and Oil stock – People with Municipal Bond but not Oil S = 35%of 2500 – 7% of 2500 = 700 Now, P ( one person investing in Municipal Bond but not in Oil Stock ) = 700 /2500 = 7/25

Re: Among a group of 2,500 people, 35 percent invest in [#permalink]
18 Jun 2012, 06:07

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For this type of question, I sometimes use a 2X2 table approach. The table is just an organized summary of the Venn diagram. Since in this case a probability is required, there is no need to calculate actual numbers. So, using percentages, we can fill out the table (see attached image). I started with 35, 18 and 7, then for example 11=18-7, 28=35-7, 82=100-18, 54=82-28, 65=100-35. There is more than one possible sequence. Necessarily, one must get the sum in the bottom row and that in the rightmost column exactly 100. In fact, you don't need to fill out the whole table, once you have that Municipal and noOil represents 28%, you are done. I present the whole table just to illustrate the use of it.

So, those who invest in Municipal and noOil stocks represent 28%=28/100=7/25.

Correct asnwer is B.

Attachments

OG13-Diagn-4.jpg [ 36.89 KiB | Viewed 5996 times ]

_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Last edited by EvaJager on 18 Jun 2012, 07:14, edited 1 time in total.

Re: Among a group of 2,500 people, 35 percent invest in [#permalink]
22 Jun 2012, 01:48

1

This post received KUDOS

Expert's post

SOLUTION

Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?

(A) 9/50 (B) 7/25 (C) 7/20 (D) 21/50 (E) 27/50

Given: 0.35*2,500=875 invest in municipal bonds; 0.07*2,500=175 invest in in both municipal bonds and oil stocks;

Therefore 875-175=700 invest in municipal bonds but NOT in in oil stocks. (Or directly: 35%-7%=28% of 2,500, which is 700, invest in municipal bonds but NOT in in oil stocks).

Re: Among a group of 2,500 people, 35 percent invest in [#permalink]
05 Mar 2014, 08:13

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