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

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04 Jul 2009, 21:47

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A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

67% (01:10) correct
33% (02:19) wrong based on 3 sessions

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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.

n(AUB) = n(A) + n(B) - n(A&B) Stmt 1: n(AUB) = 21+15-12 = 24 => 30-24 = 6 did neither report a net profit nor invest in foreign markets last year Sufficient

Stmt 2: 30-24 = 6 did not report a net profit nor invest in foreign markets last year Suffiicient

Questions like this are best solved using a simple chart:

......................./.....net profit......./........no net profit../ for. market......../..........A............./...............B........../......15 no for. market..../..........C............./...............D........./.......15 ......................./.........21............/...............9........../.......30

Note that we are being asked to find the value for D.

From here is it pretty easy to see if the statements are sufficient:

Statement 1:

Essentially we are given the value for A. Using A we can solve for C (21-A). Once we know the value for C is is very easy to find the value for D (15-C).

SUFFICIENT

Statement 2:

We are given the value of A+B+C. It is not necessary to know the individual values to solve for D: 30-(A+B+C) = D