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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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09 Feb 2014, 23:33
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Question Stats:

66% (01:40) correct 34% (01:53) wrong based on 552 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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09 Feb 2014, 23:35
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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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10 Feb 2014, 10:10
2
KUDOS
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 4293 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, 06:55, edited 1 time in total.
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Joined: 05 Feb 2014
Posts: 6
Re: Last year in a group of 30 businesses, 21 reported a net pro [#permalink]

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10 Feb 2014, 13:34
1
KUDOS
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, 15:15
1
KUDOS
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, 00:46
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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Re: Last year in a group of 30 businesses, 21 reported a net pro [#permalink]

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06 Oct 2015, 14:03
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Re: Last year in a group of 30 businesses, 21 reported a net pro [#permalink]

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08 May 2017, 05:18
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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Re: Last year in a group of 30 businesses, 21 reported a net pro   [#permalink] 08 May 2017, 05:18
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