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A marketing firm determined that, of 200 households [#permalink]
29 Dec 2007, 17:40

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200 x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Try it on other ones. It will never be confusing again.

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

200 total
80 use niether
120 use either A or B or Both
60 use only A
so 60 use B or bothAB

For every AB there are three B
3AB=B
AB+B=60
AB+3AB=60
4AB=60
AB=15

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

200 total 80 use niether 120 use either A or B or Both 60 use only A so 60 use B or bothAB

For every AB there are three B 3AB=B AB+B=60 AB+3AB=60 4AB=60 AB=15

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

Could you please post the correct formula because, the link does not open after trying hard!

In the formula A + B + neither - both, A represents all those who use brand A, not just those who use only brand A, and B represents all those who use brand B, not just those who use only brand B. So A = the number who use only brand A (60) plus the number who use both brands (x), and B = the number who use only brand B (3x) plus the number who use both brands (x):

A + B + neither - both
(60 + x) + (3x + x) + 80 - x = 200
140 + 4x = 200
x = 15

Ian, I really like this method. I got 30 on this two and like a idiot knew this was going to be wrong. I've seen this type of only A/only B questions in the OG and should have been looking out for it.

Your system seems pretty good! I'm going to start using it. Similar to the Manhattan quad system.

ian7777 wrote:

I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200 x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Try it on other ones. It will never be confusing again.

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.