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Last year in a group of 30 businesses, 21 reported a net profit and 15

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Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 05 Mar 2012, 17:27
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Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

Data Sufficiency
Question: 85
Category: Algebra First- and second-degree equations; Simultaneous equations
Page: 158
Difficulty: 650


The Official Guide For GMAT® Quantitative Review, 2ND Edition


can anybody tell the matrix approach for stmnt(2)
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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 05 Mar 2012, 22:56
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Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

Given: {Total} = {Profit} + {Investment} - {Both} + {Neither} --> 30=21+15-{Both}+{Neither} --> {Neither} = {Both} - 6.
Question: {Neither} = ?

(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets --> {Both} = 12 --> {Neither}={Both}-6=12-6=6. Sufficient.

(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both --> {Profit} + {Investment} - {Both} = 24 --> 21+15-{Both}=24 --> {Both}=12 --> {Neither}={Both}-6=12-6=6. Sufficient.

Answer: D.

TomB wrote:
can anybody tell the matrix approach for stmnt(2)

As you can see the problem can be easily solved without a matrix, but anyway here you go, matrix for statement (2):
Image
(2) says that a+b+c=24, on the other hand a+b+c+d=30=Total --> 24+d=30 --> d=6. Sufficient.

Hope it's clear.
Attachment:
30 businesses.PNG
30 businesses.PNG [ 4.79 KiB | Viewed 20402 times ]

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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post Updated on: 14 Feb 2014, 07:55
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Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.


Lets make a table to understand the given information
Attachment:
Untitled.png
Untitled.png [ 6.81 KiB | Viewed 12495 times ]


We need to find x

St1:profit and investment were 12 companies so we can find about companies with investment but nonprofit which is 3 so 3+x=9 or x=6 so sufficient


St2 means that 24 companies had shown either profit or investment or both so 30-24=6 companies with no profit and no investment
T= Only A(Profit)+ OnlyB(Investment)+ Both(investment and profit) +Neither and thus Neither= 6
Ans is D
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Last edited by WoundedTiger on 14 Feb 2014, 07:55, edited 1 time in total.
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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 04 Mar 2014, 22:00
I do not understand how can we say "last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both" when the question says "Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets."

Isn't B going against the question?

Statement in question : Last year in a group of 30 businesses, 21 reported a net profit
Statement B : last year 24 of the 30 businesses reported a net profit
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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 05 Mar 2014, 00:59
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gauravkaushik8591 wrote:
I do not understand how can we say "last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both" when the question says "Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets."

Isn't B going against the question?

Statement in question : Last year in a group of 30 businesses, 21 reported a net profit
Statement B : last year 24 of the 30 businesses reported a net profit


Refer to the matrix:
Image
a = investment and profit;
b = investment and NO profit;
c = profit and NO investment;
d = NO investment and NO profit.

(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both --> a+b+c=24 (all groups but NO investment and NO profit.).

Hope it's clear.
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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 01 Jun 2015, 03:14
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Presenting the Venn diagram approach of the solution

Interpreting the given info
We are told about 30 businesses of which 21 reported a net profit and 15 had investments in foreign markets.Refer the venn diagram below:

Image

As the total number of businesses is 30 we can write a + b + c + d = 30

Also, 21 firms reported a net profit, that would give us a + b =21. Also, it would give us c + d = 9

Similarly, 15 firms had investments in foreign markets, that would give us b + c = 15. Also it would give us a + d = 15.
We need to find the number of businesses that did not report a net profit nor invest in foreign market i.e. d. Let's see if the statements provide us the information to find a definite value of d

Statement-I
St-I tells us that 12 businesses reported net profit and had investments in foreign markets i.e. b = 12. This would give us the value of a = 9.
We know that a + d = 15 i.e. d = 6.
Hence st-I is sufficient to answer the question.

Statement-II
St-II tells us that 24 businesses reported a net profit or invested in foreign markets or both i.e. a + b + c = 24

Since a + b + c + d = 30 we can find the value of d = 6

Hence st-II is sufficient to answer the question.

Answer is option D

Hope this helps :)

Regards
Harsh
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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 02 Mar 2018, 15:48
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.



The Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of businesses, and the two characteristics are:
- had a net profit or didn't have a net profit
- invested in foreign markets or didn't invest in foreign markets

So, we can set up our diagram as follows:
Image

Now, if there are 30 businesses and 21 reported a net profit, then 9 did NOT report a net profit.
Similarly, if there are 30 businesses and 15 had investments in foreign markets, then 15 did NOT have investments in foreign markets. So, we can add that information to the diagram.
Image
Note: I placed a star in the bottom right box to remind me that this is the value we are trying to determine.

Statement 1: Last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
When we add this information to our diagram, we get the following:
Image

Since we know the sums of the rows and columns, we can determine the values in every box to get the following:
Image
Notice that we can determine the value for the bottom right box, which means we can answer the target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.
The three shaded boxes below represent the businesses that reported a net profit or invested in foreign markets, or both.
Image

Since all 4 boxes must add to 30, we can see last remaining box must contain the 6 remaining businesses.
Image
So, we can determine the value for the bottom right box, which means statement 2 is SUFFICIENT

Answer: D

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Re: Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 05 Aug 2019, 15:05
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(2) is really saying that there were 6 of 30 (30-24=6) that did not invest in foreign markets or make a profit.

From that, it is subtraction to solve that rest.
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Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 27 Dec 2019, 13:34
Bunuel wrote:
gauravkaushik8591 wrote:
I do not understand how can we say "last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both" when the question says "Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets."

Isn't B going against the question?

Statement in question : Last year in a group of 30 businesses, 21 reported a net profit
Statement B : last year 24 of the 30 businesses reported a net profit


Refer to the matrix:
Image
a = investment and profit;
b = investment and NO profit;
c = profit and NO investment;
d = NO investment and NO profit.

(2) Last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both --> a+b+c=24 (all groups but NO investment and NO profit.).

Hope it's clear.


Bunuel

When i read S2 -- per the table -- i thought the equation was 3a + b + c = 24

Here is why when i read S2

Last year 24 of the 30 businesses reported a
net profit ===================================================== this is a + c as net profit is ACROSS column 1
or invested in foreign markets ========================== this is a + b as investing in foreign markets is ACROSS row 1
or
both ========================================================= this is a as this relates to one cell one

Given the or, lets add of them up thus

- a + c + a + b + a, which is 3a + b + c

Where is the gap in my logic
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Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 28 Dec 2019, 09:44
EgmatQuantExpert wrote:
Presenting the Venn diagram approach of the solution

Interpreting the given info
We are told about 30 businesses of which 21 reported a net profit and 15 had investments in foreign markets.Refer the venn diagram below:

Image

As the total number of businesses is 30 we can write a + b + c + d = 30

Also, 21 firms reported a net profit, that would give us a + b =21. Also, it would give us c + d = 9

Similarly, 15 firms had investments in foreign markets, that would give us b + c = 15. Also it would give us a + d = 15.
We need to find the number of businesses that did not report a net profit nor invest in foreign market i.e. d. Let's see if the statements provide us the information to find a definite value of d

Statement-I
St-I tells us that 12 businesses reported net profit and had investments in foreign markets i.e. b = 12. This would give us the value of a = 9.
We know that a + d = 15 i.e. d = 6.
Hence st-I is sufficient to answer the question.

Statement-II
St-II tells us that 24 businesses reported a net profit or invested in foreign markets or both i.e. a + b + c = 24

Since a + b + c + d = 30 we can find the value of d = 6

Hence st-II is sufficient to answer the question.

Answer is option D

Hope this helps :)

Regards
Harsh



Hi EgmatQuantExpert

When i read S2 -- per the Venn Diagram -- i thought the equation for S2 was 3b + a + c = 24 (not a + b + c = 24)

Here is why when i read S2

Last year 24 of the 30 businesses reported a
net profit ===================================================== this is a + b as net profit includes the shared region as well
or invested in foreign markets ========================== this is b+c as investing in foreign markets is ACROSS the shared region as well
or
both ========================================================= this is "b" as this relates to one cell one

Given the or, lets add of them up thus

- a + b + c + b + b, which is 3b + a + c

How am i thinking through this incorrectly ?
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Last year in a group of 30 businesses, 21 reported a net profit and 15  [#permalink]

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New post 28 Dec 2019, 12:15
Hi karishma

Remembered your post regarding another overlapping set problem when thinking about S2 in this problem

Shouldn't S2 in this problem be actually saying :

Last year 24 of the 30 businesses reported a net profit ONLY or invested in foreign markets ONLY or both.


Karishma's post on the significance of 'ONLY' : https://gmatclub.com/forum/of-the-84-parents-who-attended-a-meeting-at-a-school-135191.html#p1199542

Without the "ONLY" -- there is clear overlap, is there not

Last year 24 of the 30 businesses reported a
net profit ===================================================== this is a + b as net profit includes the shared region as well
or invested in foreign markets ======================================== this is b+c as investing in foreign markets is ACROSS the shared region as well
or
both ======================================================== this is "b" as this relates to one cell one


Given the "or", lets add of them up thus

- a + b + c + b + b, which is 3b + a + c = 24

How am i thinking through this incorrectly ?

Image
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Last year in a group of 30 businesses, 21 reported a net profit and 15   [#permalink] 28 Dec 2019, 12:15
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