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# Among a group of 2,500 people, 35 percent invest in

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Math Expert
Joined: 02 Sep 2009
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Among a group of 2,500 people, 35 percent invest in [#permalink]

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14 Jun 2012, 02:49
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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
[Reveal] Spoiler: OA

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Math Expert
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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14 Jun 2012, 02:49
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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).

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

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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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14 Jun 2012, 06:09
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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.)

Attachments

m.jpg [ 9.55 KiB | Viewed 30720 times ]

Last edited by cyberjadugar on 09 Jul 2012, 01:04, edited 1 time in total.
Manager
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Posts: 156
Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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14 Jun 2012, 06:50
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

Intern
Joined: 03 Jun 2012
Posts: 31
Location: United States
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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14 Jun 2012, 20:19
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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.
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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16 Jun 2012, 03:52
Difficulty level 600+.

Probability of percentage invested in MB/ Total

35%-7%=28% of 2500= 700

P= 700/2500= 7/25
Director
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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18 Jun 2012, 07:07
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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.
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OG13-Diagn-4.jpg [ 36.89 KiB | Viewed 30489 times ]

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Last edited by EvaJager on 18 Jun 2012, 08:14, edited 1 time in total.
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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18 Jun 2012, 07:42
IMO. B same explanation as above
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Posts: 39593
Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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22 Jun 2012, 02:48
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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).

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

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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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05 Mar 2014, 09:13
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Re: Among a group of 2,500 people, 35 percent invest in [#permalink]

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28 May 2015, 16:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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11 Jun 2015, 19:59
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 ! 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

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Posts: 7439
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11 Jun 2015, 20:43
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LouieV wrote:
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 ! 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

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.

Check out overlapping sets: http://www.veritasprep.com/blog/2012/09 ... ping-sets/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews SVP Joined: 08 Jul 2010 Posts: 1733 Location: India GMAT: INSIGHT WE: Education (Education) Confusing Quant Prob [#permalink] ### Show Tags 11 Jun 2015, 20:49 1 This post received KUDOS Expert's post LouieV wrote: 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 ! 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 [Reveal] Spoiler: B Attachments File comment: www.GMATinsight.com 113.jpg [ 73.99 KiB | Viewed 17324 times ] _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html 22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Intern Joined: 11 Jun 2015 Posts: 2 Confusing Quant Prob [#permalink] ### Show Tags 11 Jun 2015, 21:46 Thank you for explaining this in such simple terms Karishma. GMATinsight, the visual was definitely a big help in allowing me to see the arithmetic behind the words. I was stomped, but I'm sure my gears will get back to speed as I progress in my preparation. THANKS EVERYONE! Math Expert Joined: 02 Sep 2009 Posts: 39593 Re: Among a group of 2,500 people, 35 percent invest in [#permalink] ### Show Tags 12 Jun 2015, 01:44 LouieV wrote: 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 ! 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! Merging topics. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html _________________ Director Joined: 10 Mar 2013 Posts: 597 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: Among a group of 2,500 people, 35 percent invest in [#permalink] ### Show Tags 04 Sep 2015, 01:59 The fastest way is from Bunuel, but in this case I would stay with percents, as it is easier to calculate: 35%-7%(overlap)=28% --> 28%/100%=7/25 Attachments PS D4.JPG [ 19.36 KiB | Viewed 13807 times ] _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Manager Joined: 10 May 2014 Posts: 141 Re: Among a group of 2,500 people, 35 percent invest in [#permalink] ### Show Tags 04 Sep 2015, 08:16 The piece of information that states that "there are 2,500 people" is completely irrelevant, right? In other words you can yield the correct answer without that piece of data. _________________ Consider giving me Kudos if I helped, but don´t take them away if I didn´t! What would you do if you weren´t afraid? Manager Joined: 01 Jun 2013 Posts: 125 GMAT 1: 650 Q50 V27 Among a group of 2,500 people, 35 percent invest in [#permalink] ### Show Tags 07 Sep 2015, 11:53 No need to calculate number of people Both OS and Muni: 7%, therefore, Muni only: 28% and OS only:11% Muni Only / All = 28%/1 >> 7/25 _________________ Please kindly click on "+1 Kudos", if you think my post is useful Manager Joined: 17 Mar 2014 Posts: 167 Location: United States Concentration: Entrepreneurship, Leadership GPA: 3.97 Re: Among a group of 2,500 people, 35 percent invest in [#permalink] ### Show Tags 08 Dec 2015, 09:29 Bunuel wrote: 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 For this Q - I was thinking why cant we assume that "35%" mentioned only include people that invest in municipal bonds. But Karishma from Veriats cleared the doubt. ONLY should have been mentioned - if that was the case. Below excerpts of her reply - "Yes, if they say, "35% invest in municipal bonds only and 7% invest in both," then the two are mutually exclusive." _________________ KUDOS!!!, I need them too Re: Among a group of 2,500 people, 35 percent invest in [#permalink] 08 Dec 2015, 09:29 Go to page 1 2 Next [ 23 posts ] Similar topics Replies Last post Similar Topics: 2 A school must raise exactly$2,500 over the next year by investing a 3 19 Mar 2017, 08:14
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