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

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

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

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New post 10 Feb 2014, 10:10
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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 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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Re: Last year in a group of 30 businesses, 21 reported a net pro [#permalink]

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New post 10 Feb 2014, 13:34
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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)

Answer 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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New post 10 Feb 2014, 15:15
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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.


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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New post 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.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 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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New post 08 May 2017, 05:18
Hello from the GMAT Club BumpBot!

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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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