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# Last year in a group of 30 businesses, 21 reported a net pro

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Math Expert
Joined: 02 Sep 2009
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Last year in a group of 30 businesses, 21 reported a net pro  [#permalink]

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10 Feb 2014, 00:33
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45% (medium)

Question Stats:

69% (01:38) correct 31% (01:52) wrong based on 563 sessions

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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.

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

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

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10 Feb 2014, 00:35
2
2
SOLUTION

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.

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

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Updated on: 14 Feb 2014, 07:55
2
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 [ 6.81 KiB | Viewed 5396 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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Originally posted by WoundedTiger on 10 Feb 2014, 11:10.
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 pro  [#permalink]

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10 Feb 2014, 14:34
1
The answer becomes easy by drawing a venn diagram.

From (i) and given info The net profit circle should have a total of 21( 9+12) and investment circle of 15 (12+3). Subtract 9 +12+3 from 30.
Similarly for (ii)

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

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10 Feb 2014, 16:15
1
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.

So we know that 21 reported net profit and 15 had investments in foreign markets.
$$21+15=36$$ we see its above 30, and we know that they could be overlapping.

Lest see St(1): 12 businesses reported a net profit and had investments in foreign markets.
So this is the overlap! Great. $$36-12=24$$. Sufficient.

St(2) 24 businesses reported a net profit or invested in foreign markets, or both. That give us the ansewer stright away. Sufficient.

So ans is D.
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Re: Last year in a group of 30 businesses, 21 reported a net pro  [#permalink]

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17 Feb 2014, 01:46
SOLUTION

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.

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

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02 Mar 2018, 15:48
Top Contributor
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:

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.

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:

Since we know the sums of the rows and columns, we can determine the values in every box to get the following:

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.

Since all 4 boxes must add to 30, we can see last remaining box must contain the 6 remaining businesses.

So, we can determine the value for the bottom right box, which means statement 2 is SUFFICIENT

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Last year in a group of 30 businesses, 21 reported a net pro &nbs [#permalink] 02 Mar 2018, 15:48
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