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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 09 Oct 2008, 04:44
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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: math--net profit [#permalink] New post 09 Oct 2008, 04:53
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both are sufficient:

C
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Re: math--net profit [#permalink] New post 09 Oct 2008, 08:11
I think the answer is C(both statements alone is sufficient)

Explanation:
==========
1)
if 12 out of 30 businesses reported a profit with intl investments, then there are 3 businesses with intl investments and no profits.
Also there will be 9 businesses with no intl investments and on profits. finally that leaves 6 businesses with no profits and no intl investments.

2)if 24 businesses have intl investments and/or on profits then that leaves 6 business with neither of them

Hope this helps,
SM
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Re: math--net profit [#permalink] New post 09 Oct 2008, 08:55
albany09 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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.



I think the answer is D

statement 1: 12 reported a net profit and invested in foreign markets.
businesses reporting a net profit= 21-12=9
businesses invested in foreign market=15-12=3
total businesses reporting net profit, investing in foreign markets or both=12+9+3=24

therefore businesses that did not report a net profit nor invested in foreign market=30-24=6

statement 2 gives the figure 24 which leaves 6 busineses that did not report net profit nor invested in foreign markets.
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Re: math--net profit [#permalink] New post 09 Oct 2008, 09:10
Hi guys,

my contribution:

From the question we can draw the following matrix

Code:
                  report Net Prof.            no report Net Prof.         Total
Invest                   x                                z                         15
No Invest               y                               w                         15
Total                     21                              9


the question asks for w

From 1

x=12, thus y=9 thus w=6

SUFF.



From 2

x+y+z=24, thus w=6

SUFF.

D

OA?

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Re: math--net profit [#permalink] New post 09 Oct 2008, 10:02
Answer is D :twisted:

Each of them alone is sufficient

Quickly draw Van Diagram [ ( 25 ( ) 15 ) ] = 30

All you need is combined set of A and B, which is A + B - intersection of A and B.
1) give you intersaction of A + B (SUFFICIENT)
2) give you combined (SUFFICIENT)

No calcuation needed.
Re: math--net profit   [#permalink] 09 Oct 2008, 10:02
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