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

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.

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.

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/

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

Bunuel is there a shortcut to calculate percent when it comes to big numbers. Quote time consuming....

\(0.35*2,500=875\) invest in municipal bonds;
\(0.07*2,500=175\) invest in in both municipal bonds and oil stocks;

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

Hi , as the question asked for the probability you can think that it will be fractions so we don't actually need to deal with numbers.
Only calculating percentages is sufficient.{checkout ENGRTOMBA2018 's answer regarding this.It is much more simple and takes less time to solve }
Hope it helps.

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.

To calculate the probability that a person selected invests in municipal bonds but not in oil stocks, we need to subtract the percentage of people who invest in both municipal bonds and oil stocks from the percentage of people who invest in municipal bonds.

Given:

Percentage of people who invest in municipal bonds = 35%
Percentage of people who invest in oil stocks = 18%
Percentage of people who invest in both municipal bonds and oil stocks = 7%
To find the percentage of people who invest in municipal bonds but not in oil stocks, we subtract the percentage of people who invest in both from the percentage of people who invest in municipal bonds:

Percentage of people who invest in municipal bonds but not in oil stocks = Percentage of people who invest in municipal bonds - Percentage of people who invest in both municipal bonds and oil stocks = 35% - 7% = 28%