Data Sufficiency

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.

Ans :- B.

I got a by concept of 4 different things then make table concept. Plz help.

30 businesses. 21 reported net profit. 15 invested in foreign markets. How many did neither?

Look at the attached Venn diagram:

We have -->

P + B = 21 ....1
F + B = 15 .....2
P + F + B + N = 30 ....3

We need to find N.

Statement 1:

12 reported net profit and had investments in foreign markets.
This gives us the value of B = 12

From 1: P = 9
From 2: F = 3
Therefore from 3: N = 6
SUFFICIENT

Statement 2:

24 out of 30 reported netprofit or invested in foreign markets or both.

This means P + F + B = 24

So obviously N = 6
SUFFICIENT


Answer is D. I don't know why OA is B, looking forward to more explanations.

I didn't get ur answer for second statement. since we are not sure that whether those 24 out of 30 reported are for netprofit or invested in foreign markets or both. so we cannot put them in picture. Thatswhy i have ignored B statement and gone with A.

albatross86 wrote:30 businesses. 21 reported net profit. 15 invested in foreign markets. How many did neither?

Look at the attached Venn diagram:

We have -->

P + B = 21 ....1
F + B = 15 .....2
P + F + B + N = 30 ....3

We need to find N.

Statement 1:

12 reported net profit and had investments in foreign markets.
This gives us the value of B = 12

From 1: P = 9
From 2: F = 3
Therefore from 3: N = 6
SUFFICIENT

Statement 2:

24 out of 30 reported netprofit or invested in foreign markets or both.

This means P + F + B = 24

So obviously N = 6
SUFFICIENT


Answer is D. I don't know why OA is B, looking forward to more explanations.

Oops sorry I forgot to attach the Venn diagram!

Anyway, Statement 2 says 24 reported on net profit or invested in foreign markets or both. This means 30-24 = 6 invested in neither, since the 24 accounts for all the other possibilities.

P - Only Net profit
F - Only invested in foreign market
B - Both
N - Neither

So P+F+B = 24