OG Problem.. Please help

[NehaBhandari]

A marketing firm determined that out 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. How many of the 200 households surveyed use both brands..

1)15
2)20
3)30
4)40
5)45

Can someone use the formula

T=G1+G2-Both+Neither

and come to the right answer..... Please give ur explainations.. I am not geting the ansswer when I apply the formula..Your hlp is appreciated

[brb588]

I don't think it's necessary. You're trying to find out how many people use both brands. Start with 200 people. 80 pf them use nothing, so subtract it from 200 and get 120. 60 used only brand A, so subtract 60 from 120, and you have 60 left.

Now it's simple algebra. Let x = the amount of people who use both brands. The problems says for every one person that uses both, 3 use only B. Therefore:

3x + x = 60, x = 15

The amount that use both brands is 15, choice A.

[NehaBhandari]

True.. But I need to know why the above formula fails.. am i missing some concept.

By applying the formula
T= G1+G2 -Both+Neither
200= 60+3x-x+80
60 = 2x
x =30 which is wrong OA is A


Am I doing something wrong here.. plz help!!

[dmateer25]

True.. But I need to know why the above formula fails.. am i missing some concept.

By applying the formula
T= G1+G2 -Both+Neither
200= 60+3x-x+80
60 = 2x
x =30 which is wrong OA is A


Am I doing something wrong here.. plz help!!

The formula doesn't work because the question says that 60 used only Brand A soap.

Total = Only A + Only B + AB + Neither

Let x = those that AB

200 = 60 + 3x + x + 80
200 = 140 + 4x
60=4x
15=x

[brb588]

I just found out that the formula is switched up for this question

https://www.manhattangmat.com/forums/post4973.html

[NehaBhandari]

Great!!.. Thanks for the help guys...I need to know some serious stuff here ..

Thanks again.. keep replying