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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]

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15 Mar 2011, 00:34
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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 business reported a net profit but did not invest in foreign markets?

(1) Last year 10 of the business both reported a profit and had investments in foreign markets.
(2) Last year 4 of the business did not report a net profit nor invest in foreign markets

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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Re: 294. Last year in a group of 30 businesses, 21 reported a ne [#permalink]

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15 Mar 2011, 00:56
n(P) = Number of businesses showed net profits = 21
$$n(P\cap F)$$ = Number of businesses made foreign investments and had net profits
$$n(Neither)$$ = Number of businesses who neither made foreign investments nor had any net profits
$$n(Total) =$$ Total number of businesses = 30

Formula;
$$n(Total) = n(P) + n(F) - n(P\cap F) + n(Neither)$$
$$30=21+15-n(P\cap F)+n(Neither)$$ ----- 1

To find;
Number of businesses that reported ONLY net profit but had no foreign investment

If we find $$n(P\cap F)$$, then we would know the above information.

1. $$n(P\cap F)$$ = 10
Thus,
Number of businesses that reported ONLY net profit but had no foreign investment = n(P) - 10 = 21-10 = 11
Sufficient.

2. $$n(Neither)$$ = 10
Substituting it in the equation 1, we will get;
$$n(P\cap F) = 10$$
Thus,
Number of businesses that reported ONLY net profit but had no foreign investment = n(P) - 10 = 21-10 = 11
Sufficient.

Ans: "D"
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Re: 294. Last year in a group of 30 businesses, 21 reported a ne [#permalink]

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15 Mar 2011, 04:05
Let P -> Business that reported a net profit

30 = P + I - Both + Neither

From (1) -> Business that reported a net profit but did not invest in foreign markets = 21 - 10 = 11 , so sufficient.

From (2) 30 = 21 + 15 - both + 4

=> both = 40 - 30 = 10

So again, business that reported a net profit but did not invest in foreign markets = 21 - 10 = 11, so (2) is suffficient.

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

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17 Jan 2012, 10:34
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink]

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22 Dec 2012, 02:05
Bunuel,
Can this be solved using double set matrix?
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Re: Last year in a group of 30 businesses, 21 reported a net [#permalink]

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22 Dec 2012, 04:54
Sachin9 wrote:
Bunuel,
Can this be solved using double set matrix?

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Re: Last year in a group of 30 businesses, 21 reported a net   [#permalink] 22 Dec 2012, 04:54
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