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

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Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 28 Jan 2007, 07:46
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-in-a-group-of-30-businesses-21-reported-a-net-128640.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 03 Aug 2012, 23:57, edited 2 times in total.
Edited the question and added the OA.
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 [#permalink] New post 28 Jan 2007, 08:08
A group problem.

A + B - both + neither = total

21 + 15 - both + neither = 30

(1)

both = 12

suff AD

(2)

A + B - both = 24

suff

The answer is D
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 [#permalink] New post 29 Jan 2007, 02:35
adub35 wrote:
A group problem.

A + B - both + neither = total

21 + 15 - both + neither = 30

(1)

both = 12

suff AD

(2)

A + B - both = 24

suff

The answer is D


Text book explanation: D it is.
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 03 Aug 2012, 23:38
Hi, Can someone please walk me through how values provided in statement 2 can be put into Grid method used for solving such questions

Thanks
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink] New post 03 Aug 2012, 23:55
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imhimanshu wrote:
Hi, Can someone please walk me through how values provided in statement 2 can be put into Grid method used for solving such questions

Thanks


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.

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-in-a-group-of-30-businesses-21-reported-a-net-128640.html
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Re: Last year in a group of 30 businesses, 21 reported a net   [#permalink] 03 Aug 2012, 23:55
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