Please throw some light on this question below

D6

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

Choices
A. 15
B. 20
c. 30
d. 40
e. 50

step 1) Venn diagram or double set matrix (use matrix for MGMAT way - Venn used only for sets of 3)

step 2) first try T=G1 + G2 + n - Both


Why did 200=60+3B+80-B (not work out)

answer is A 15 ?

Tricky. I love that both-neither formula... but it has to be adjusted for this problem because of the set-up.

The formula is:
Total = Group 1 + Group 2 + Neither - Both.

Group 1 in this case we'll call Brand A and Group 2 will be Brand B. Group 1 includes EVERYONE who uses Brand A, not just the people who ONLY use Brand A. Ditto for Group 2 / Brand B. And this is where the formula breaks down: the value given in the problem for Brand B (3x) is for those using ONLY Brand B, not EVERYONE using Brand B. The formula assumes the two Groups INCLUDE the "Both" people, which is why it subtracts them out at the end. But we don't need to subtract out the overlap if the overlap is not included in the two Groups - just the opposite, we need to add the "Both" people in because they haven't been counted in the two Groups.

The figure given for Brand A is also for those who ONLY use A, so we need to change the formula to:
Total = Group 1 + Group 2 + Neither + Both (because we haven't yet counted the 'Both' people elsewhere in the formula).

200 = 60 + 3B + 80 + B
200 - 140 = 4B
60 = 4B
B = 15

Hi Stacey,

I was wondering if you help explain how to derive the solution using the Double-Set Matrix? I got completely thrown-off by the 3x element!

A NOT A TOTAL
B X 60 3X
NOT B 80
TOTAL 60 140 200

So hard to show these on the format-challenged forums. From the problem:

-----------A-----NOT A------ TOTAL
B----------X------ 3X--------- 3X + X
NOT B-----60-----80 -------?
TOTAL ---?----- --?------- 200

Then, start to calculate:
-----------A-----NOT A------ TOTAL
B----------X------ 3X--------- 4X
NOT B-----60-----80 -------140
TOTAL ---?----- --?------- 200

Write a formula: 4X + 140 = 200
and solve: 4x = 60
x = 15

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5,000 have been vaccinated against both, how many have been vaccinated only against rubella?

A. 2,500
B. 7,500
C. 10,000
D. 15,000
E. 17,500

Please check answer choice A,is it 25000?

The Venn Diag is the mundane option. Let answer choice A remain at whatever it is in all its glory

The question setter is thinking of C as the correct answer and so it is.

The clue for the quick fix is "5,000 have been vaccinated against both". Therefore, measles alone is 2500,total measles is 7500, total rubella is 15000 and rubella alone is 15000-5000=10000.

Please source the second question - if it is an OG question, please list the book name and question number. If it is not OG, please list the author.

If this isn't done, we will have to delete the question and all of its commentary as we have certain sources from which we do not have legal permission to post questions.

Thanks!