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

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SVP
Joined: 04 May 2006
Posts: 1926
Schools: CBS, Kellogg
Followers: 20

Kudos [?]: 656 [0], given: 1

Last year in a group of 30 businesses, 21 reported a net [#permalink]  01 Jun 2009, 18:23
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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.

Want to make sure that Oa is wrong!
_________________
Manager
Joined: 08 Feb 2009
Posts: 146
Schools: Anderson
Followers: 3

Kudos [?]: 38 [0], given: 3

Re: Sets [#permalink]  01 Jun 2009, 18:38

Total = N = Profit + Not Profit = Invest + Not Invest

If you draw out a chart, it is easier.

(1) 30 = 21 + 9 = 15 + 15

If 12 reported Profit and Invested, 15-12 = 3 Invested, but Not Profit.
Not Profit = 9.
Not Profit - Invest, Not Profit = 9 - 3 = 6.
SUFFICIENT.

(2)
This is straightforward.
30 - 24 = 6
SUFFICIENT.
Manager
Joined: 13 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 5

Kudos [?]: 29 [0], given: 1

Re: Sets [#permalink]  01 Jun 2009, 21:00
sondenso wrote:
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.

Want to make sure that Oa is wrong!

Variables:
$$P$$ - net profit
$$F$$ - foreign markets
$$B$$ - both
$$X$$ - neither

Given:
$$P+B+F+X=30$$

$$P+B=21$$

$$F+B=15$$

Question:$$(X?)$$

(1) $$B=12$$

(2) $$P+F+B=24$$

We're given 3 equations, we just need 1 more. Either fact gives us this.

Final Answer, $$D$$.
_________________

SVP
Joined: 04 May 2006
Posts: 1926
Schools: CBS, Kellogg
Followers: 20

Kudos [?]: 656 [0], given: 1

Re: Sets [#permalink]  02 Jun 2009, 00:34
sondenso wrote:
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.

Want to make sure that Oa is wrong!

Variables:
$$P$$ - net profit
$$F$$ - foreign markets
$$B$$ - both
$$X$$ - neither

Given:
$$P+B+F+X=30$$

$$P+B=21$$

$$F+B=15$$

Question:$$(X?)$$

(1) $$B=12$$

(2) $$P+F+B=24$$

We're given 3 equations, we just need 1 more. Either fact gives us this.

Final Answer, $$D$$.

Agree, D should be the OA
OA wrong!
_________________
Manager
Joined: 13 May 2009
Posts: 195
Schools: Stanford, Harvard, Berkeley, INSEAD
Followers: 5

Kudos [?]: 29 [0], given: 1

Re: Sets [#permalink]  02 Jun 2009, 00:54
sondenso wrote:
sondenso wrote:
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.

Want to make sure that Oa is wrong!

Variables:
$$P$$ - net profit
$$F$$ - foreign markets
$$B$$ - both
$$X$$ - neither

Given:
$$P+B+F+X=30$$

$$P+B=21$$

$$F+B=15$$

Question:$$(X?)$$

(1) $$B=12$$

(2) $$P+F+B=24$$

We're given 3 equations, we just need 1 more. Either fact gives us this.

Final Answer, $$D$$.

Agree, D should be the OA
OA wrong!

Where are you getting these from?
_________________

Re: Sets   [#permalink] 02 Jun 2009, 00:54
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# Last year in a group of 30 businesses, 21 reported a net

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