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

dave13 · Answer

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;

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

SonGoku · Answer

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.

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.

ArnauG · Answer

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%

DanTheGMATMan · Answer

Overlapping sets phrased as a probability:

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

Duncomo · Answer

Hi people is there any way to tell that for this question the 7% is included in both the 35 and the 18. There is no phrase such as "of those" it just says and, which to me you could interpret this either way. Is it a case of if there isn't clear evidence that these 7% are more people, then assume it's the overlapping style question. Came here from official practice because B and C are the clear choices but Im not sure on test day which of those I would choose (the 35% answer or the 28% one)

Bunuel · Answer

You are overcomplicating it. The problem never says only. So 35 percent means everyone who buys bonds, including those who also buy oil. Likewise 18 percent means everyone who buys oil, including those who also buy bonds. The 7 percent are the same people counted in both groups.

Duncomo · Answer

Thanks Bunuel, I think it's the word "and" that lost my confidence here. To me that and indicated this as a separate group. Would I be right in saying that unless it explicitly says otherwise, assume the third part here (7% in this case) means as it does here, to take 7 away from the 35% and look for something equal to 28%?

Bunuel · Answer

I don’t really follow what you’re trying to say. 7% invest in both simply means 7% invest in both. I don’t understand what additional or separate group you’re referring to. Also, 35% invest in municipal bonds doesn’t mean 35% invest only in municipal bonds. So I don’t really see where the confusion comes from.

Duncomo · Answer

sorry let me try be clearer my bad, " 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..." The "and" here to me could imply that of those 2500 people, 42% (35+7) invest in municipal bonds and 25% (18+7) invest in oil stocks. As if they are 3 separate groups in the question.

Bunuel · Answer

The “and” there doesn’t mean anything special. It’s just joining three parts of the sentence: 35% invest in municipal bonds, 18% in oil stocks, and 7% in both. It doesn’t mean the 7% is added to anything. Also, again, 35% invest in municipal bonds never means 35% invest only in municipal bonds. If it were only, it would clearly say “only.”

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

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

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