Last visit was: 31 Oct 2024, 16:03 It is currently 31 Oct 2024, 16:03
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
505-555 Level|   Overlapping Sets|   Percent and Interest Problems|   Probability|                        
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
Given Kudos: 87,883
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,098
 [182]
15
Kudos
Add Kudos
166
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
Given Kudos: 87,883
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,098
 [45]
23
Kudos
Add Kudos
22
Bookmarks
Bookmark this Post
User avatar
cyberjadugar
Joined: 29 Mar 2012
Last visit: 28 May 2024
Posts: 266
Own Kudos:
1,561
 [33]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Posts: 266
Kudos: 1,561
 [33]
24
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
User avatar
EvaJager
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 516
Own Kudos:
2,190
 [20]
Given Kudos: 43
WE:Science (Education)
Posts: 516
Kudos: 2,190
 [20]
15
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
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
OG13-Diagn-4.jpg [ 36.89 KiB | Viewed 111637 times ]

General Discussion
User avatar
gmatdog
Joined: 03 Jun 2012
Last visit: 06 Jul 2012
Posts: 22
Own Kudos:
156
 [4]
Given Kudos: 2
Location: United States
WE:Project Management (Computer Software)
Posts: 22
Kudos: 156
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
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.
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 31 Oct 2024
Posts: 15,420
Own Kudos:
69,198
 [8]
Given Kudos: 446
Location: Pune, India
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 15,420
Kudos: 69,198
 [8]
7
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
LouieV
Hello everyone and thank you for this forum!!!

I admit it has been a few years since I've sat down to attack standardized test, but my GOODNESS :shock: ! Can someone please lend some wisdom on this problem from TOG 2016 pg 20 #4.

Among a group of 2500 people, 35% invest in municipal bonds, 18% invest in oil stocks, and 7% invest in both municipal bonds and oil stocks. If 1 person is randomly selected from the 2500 people, what is the probability that the person 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

Thanks in advance!

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/
User avatar
GMATinsight
User avatar
GMAT Club Legend
Joined: 08 Jul 2010
Last visit: 27 Oct 2024
Posts: 6,055
Own Kudos:
14,392
 [3]
Given Kudos: 125
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,055
Kudos: 14,392
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
LouieV
Hello everyone and thank you for this forum!!!

I admit it has been a few years since I've sat down to attack standardized test, but my GOODNESS :shock: ! Can someone please lend some wisdom on this problem from TOG 2016 pg 20 #4.

Among a group of 2500 people, 35% invest in municipal bonds, 18% invest in oil stocks, and 7% invest in both municipal bonds and oil stocks. If 1 person is randomly selected from the 2500 people, what is the probability that the person 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

Thanks in advance!

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
Attachments

File comment: www.GMATinsight.com
113.jpg
113.jpg [ 73.99 KiB | Viewed 96714 times ]

User avatar
dave13
Joined: 09 Mar 2016
Last visit: 22 Oct 2024
Posts: 1,134
Own Kudos:
Given Kudos: 3,851
Posts: 1,134
Kudos: 1,047
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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).

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


Answer: B.

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;
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 31 Oct 2024
Posts: 19,675
Own Kudos:
23,711
 [2]
Given Kudos: 287
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,675
Kudos: 23,711
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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

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
User avatar
SonGoku
Joined: 11 May 2018
Last visit: 25 Dec 2022
Posts: 123
Own Kudos:
84
 [1]
Given Kudos: 287
Products:
Posts: 123
Kudos: 84
 [1]
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dave13
Bunuel
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).

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


Answer: B.

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;
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.
User avatar
Basshead
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 943
Own Kudos:
Given Kudos: 432
Location: United States
Posts: 943
Kudos: 245
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Attachments

2500percent.PNG
2500percent.PNG [ 10.19 KiB | Viewed 31096 times ]

User avatar
ArnauG
Joined: 23 Dec 2022
Last visit: 14 Oct 2023
Posts: 303
Own Kudos:
Given Kudos: 199
Posts: 303
Kudos: 39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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%
User avatar
DanTheGMATMan
Joined: 02 Oct 2015
Last visit: 31 Oct 2024
Posts: 281
Own Kudos:
Given Kudos: 9
Expert reply
Posts: 281
Kudos: 71
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­Overlapping sets phrased as a probability:

­
Moderator:
Math Expert
96533 posts