Workers are grouped by their areas of expertise and are placed on at least one

team. There are 20 workers on the Marketing team, 30 on the Sales team, and 40

on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers

are on both the Sales and Vision teams, 9 workers are on both the Marketing

and Vision teams, and 4 workers are on all three teams. How many workers are

there in total?

]]>In your post where you state the formula for 3 sets, does overlap of 1&2 include overlap of 1&2&3 also? ]]>

As you pointed out, the first problem can be narrowed down to D or E: The formula would look like this:

Total = Chem + Bio – Both + Neither

200 = 130 + 150 – B + N

We know that N must be at least 30, so let’s see what happens when N=30:

200 = 130 + 150 – B + 30

200 = 310 – B

B = 110

Even if you’re not sure whether 110 is the highest or lowest B could possibly be, it doesn’t matter, because you know it’s a boundary point of the range, which means only answers D or E could be correct.

Then, the trick is to realize that B could not be greater than 130, because even if every chem major was also a bio major, there are only 130 chem majors total. D is the winner.

Regarding the second problem, if T represents televisions, L represents laptops, S represents stereos, and N represents none of them, the formula would look like this:

T + L + S – (Overlap of T and L) – (Overlap of T and S) – (Overlap of L and S) – [2 * (Overlap of all three)] + N = total

75 + 50 + S – (Overlap of T and L) – (Overlap of T and S) – (Overlap of L and S) – 2 * 20 + N = 150

There are two catches here: 1. The remaining overlaps can be combined, because we’re told that “45 households have exactly two of the three devices”; 2. We’re told that “the number of households that have stereos is four times the number of households that have none of the three devices”, so we know that N=S/4. (You could also substitute 4N for S, but keep in mind that you’re looking for S in the end).

Substitute:

75 + 50 + S – 45 – 2*20 + S/4 = 150

125 + S – 45 – 40 + S/4 = 150

40 + S + S/4 = 150

5S/4 = 110

5S=440

S=88

]]>i m getting option D

here ,given that atleast 30 are not majoring in either.

let X are majoring in both.then ,13-X +150-X +X=170

=>X=110

now,Max no. of people who do not major in either would be when those who major in Chemistry overlap fully with the ones who major in Biology.

so,atmost 50 people do not major in any subject.

with this info,i get X=130

so the range will be 110<=Xthose who have stereo =4X

so equation would be like,

75+4X-a-20+50-20-c-b+X=150

putting a+b+c=45,we get

X=22

=>4X=88,so option B.

sir, i would request if u please enlighten us with finding Maximum /Minimum values in this same genre of questions. ]]>

T= 200

Ch = 130

Bio = 150

N = 30

Both Ch and Bio = ?

T = Ch + Bio – B + N

200 = 130 + 150 – B + 30

B = 110

Hence, we are down to answer choices D & E.

The range can calculated from the given number of students in Ch and Bio as maximum number of students who can major in both is the students of Chemistry.

So, the answer is D