Among a group of 2,500 people, 35 percent invest in municipal bonds, 1

Question

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

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

Bunuel · Accepted Answer

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

(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).

P=\frac{Favorable}{Total}=\frac{700}{2,500}=\frac{7}{25} .

Answer: B.

cyberjadugar · Answer

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.)

Answer is (B)

EvaJager · Answer

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.

gmatdog · Answer

Percentage investing in Municipal bonds = 35%
Percentage investing in both = 7%
Percentage investing in ONLY Municipal bonds = (35-7)% = 28%

Therefore, Probability of selecting one who invests Only in Municipal bonds = 28% = 28/100 = 7/25. 
Answer (B) is correct.

KarishmaB · Answer

So this question actually pertains to overlapping sets. Say, there are 100 people instead (since we have percentages) Number of people investing in MB = 35 Number of people investing in OS = 18 Number of people investing in both = 7 So how many people invest in MB but not OS? 35 invest in MB but 7 invest in both (so out of 35, 7 invest in OC too). We need to remove these 7 since we need the number of people who invest in MB only. We get 28. So 28 out of 100 people invest in only MB. So out of 100, if we pick one person, the probability that he invests in MB only is 28/100 = 7/25 The probability remains same no matter how many people there are - 100 or 2500 or 500000 etc. Answer (B) Check out overlapping sets: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/09 ... ping-sets/

GMATinsight · Answer

Total People = 2500 people

35% invest in municipal bonds, i.e Probability of Investing in Mutual Bonds = 0.35
i.e. i.e Probability of NOT Investing in Mutual Bonds = 0.65

18% invest in oil stocks i.e Probability of Investing in Oil stock = 0.18
i.e Probability of NOT Investing in Oil stock = 0.82

7% invest in both municipal bonds and oil stocks = 0.07

i.e. we can conclude that Probability of NOT investing in any one of them = 1-(0.35+0.18+0.07) = 0.54

Probability of Investing in Mulual Bond but NOT in Oil Stock = 0.82-0.54 = 0.28 = 28/100 = 7/25

Answer: Option  B

ScottTargetTestPrep · Answer

The number of people who invest in ONLY municipal bonds is:

2,500 x 0.35 - 2,500 x 0.07

2,500(0.35 - 0.07) = 2,500(0.28) = 700

So, the probability that the person selected will be one who invests in municipal bonds and NOT in oil stocks is 700/2500 = 7/25.

Answer: B

Basshead · Answer

The key here is not to spend precious time converting the percentages. If we let the total = 100, we can determine that the percentage of people that invest in muni bonds & doesn't invest in oil stocks = 28.

28/100 = 7/25

This question should take less than a minute we simply keep the percentages.

DanTheGMATMan · Answer

Overlapping sets phrased as a probability:

https://www.youtube.com/watch?v=BjyfadPW474

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=KyINqiYFUrU Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

SKS27 · Answer

Hi EvaJager,

Could you explain when it is preferred to use the Venn diagram and the 2x2 matrix to solve overlapping sets questions?

Many thanks!

dostwal · Answer

Visualising this problem as overlapping set or 2 set venn diagram can make it solve faster - we're asked on the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks which will be = [28]*2500[/100] divided by total number that is 2500. Simplifying this gives 7/25

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Among a group of 2,500 people, 35 percent invest in municipal bonds, 1

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