Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Attend a Veritas Prep GMAT Class for Free. With free trial classes you can work with a 99th percentile expert free of charge. Learn valuable strategies and find your new favorite instructor; click for a list of upcoming dates and teachers.

Join us for a debate on how these elite MBA programs are different from each other, what are their strengths & weaknesses, and how to decide which one is better for you.

Join us for a debate between the two MBA experts on how these elite MBA programs are different from each other, what are their strengths & weaknesses, and how to decide which one is better for you.

Only 2000 test-takers score 760 or higher annually. These students not only secure admissions at top B-schools, but they also get an estimated $100M in scholarships. Find out more...

A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

25 Jun 2012, 01:28

8

94

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

66% (01:45) correct 34% (02:12) wrong based on 2871 sessions

HideShow timer Statistics

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Diagnostic Test Question: 6 Page: 21 Difficulty: 650

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

25 Jun 2012, 01:28

12

12

SOLUTION

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Given:

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) --> \(x=15\).

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

28 Jun 2012, 01:41

6

1

pallavisatsangi wrote:

Shouldn't the answer be [C]

60(Brand A) +3x(Brand B)-x(Both Brands) = 200-80(total is 120 since 80 use neither)

60+2x = 120 => x =30

No pallavisatsangi The answer is A (15) you can not subtract x (both using A and B) Because in the question it is mentioned that 60 people is only brand A and accordingly 3x people use only Brand B.... if the term 'ONLY' had not been used in the question then you would have subtracted x .. but since in both cases term 'only' has been used, you can not subtract x So eq. becomes 60 +x+3x+80=200 x=15

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

13 Aug 2012, 06:02

5

Nice question, i took around 1 minute to comprehend this line "for every household that used both brands of soap, 3 used only Brand B soap" and still over looked the word "only" Brand B. I chose (C)30 , but it should be 15. Nice explanation every one. One important thing i observed in these questions, in which we have to deal with Only A/ Only B type issues that it is better to go with Venn-Dia. rather than table as it adds to complexity (only A-->not B)and consumes more time than former. On the other hand, the table is easier to work with when the questions deal with "both/neither-nor" elements, range of elements. Just my opinion.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

04 Sep 2012, 17:11

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?

A) 15 B) 20 C) 30 D) 40 E) 45

If someone could tell me how to solve the problem using the manhattan method (with grids), that would be awesome. For such a simple problem, I can't figure out how I'm messing up setting up the grid.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

04 Sep 2012, 23:24

1

egiles wrote:

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?

A) 15 B) 20 C) 30 D) 40 E) 45

If someone could tell me how to solve the problem using the manhattan method (with grids), that would be awesome. For such a simple problem, I can't figure out how I'm messing up setting up the grid.

The data in your table should be as follow:

x 3x 60 60 80 140 60+x 80+3x 200

From the first line, x + 3x = 60 (the same equation can be obtained using the last line - 60 + x + 80 + 3x = 200).

Your mistake was misplacing 60 - it is the number of households using only brand A (meaning A but not B).
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

Updated on: 02 Jan 2019, 12:16

Top Contributor

1

Bunuel wrote:

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Here's a step-by-step approach using the Double Matrix method.

Here, we have a population of 200 households , and the two characteristics are: - using or not using Brand A soap - using or not using Brand B soap

So, we can set up our matrix as follows (where "~" represents "not"):

80 used neither Brand A nor Brand B soap We can add this to our diagram as follows:

60 used only Brand A soap We get...

At this point, we can see that the right-hand column adds to 140, which means 140 households do NOT use brand B soap.

Since there are 200 households altogether, we can conclude that 60 households DO use brand B soap.

For every household that used BOTH brands of soap... Let's let x = # of households that use BOTH brands....

...3 used only Brand B soap. So, 3x = # of households that use ONLY brand B soap

At this point, when we examine the left-hand column, we can see that x + 3x = 60 Simplify to get 4x = 60 Solve to get x = 15

How many of the 200 households surveyed used BOTH brands of soap? Since x = # of households that use BOTH brands of soap, the correct answer here is: A

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

08 Feb 2017, 10:33

2

Bunuel wrote:

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

This is an overlapping set question. A great way to solve this problem is to set up a table with two main categories: Brand A and Brand B. More specifically, our table will be labeled as follows:

1) Brand A

2) No Brand A

3) Brand B

4) No Brand B

We are given that of 200 households surveyed, 80 did not use either brand and 60 used only Brand A. We are also given that for every household that used both brands, 3 used only Brand B. Thus, we can let x = the number of households that used both brands and 3x = the number of households that only used Brand B. We need to determine how many households used both brands.

Let’s fill all of this into our table.

We can create the following equation with the “Total” column and determine x:

4x + 140 = 200

4x = 60

x = 15

Thus, 15 households used both brands of soap.

Alternative solution:

This is an overlapping set question. We can use the following formula:

Total = A only + B only + Both + Neither

We are given that the Total = 200, A only = 60, and Neither = 80. We are given that for every household that used both brands of soap, 3 used only Brand B. So, if we let x = Both, then 3x = B only. Thus:

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

16 Nov 2017, 00:47

Bunuel wrote:

SOLUTION

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Given:

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) --> \(x=15\).

Answer: A.

Can you please explain "if x used both A and B, then 3x used only B (but not A).So, \(4x+140=200\) --> \(x=15\)" I can't comprehend this part. it is specifically mentioned in the question that 3 used 'only' brand B soap. So, why it is dependable on "both brands of soap" part. if so, why isn't 60 written as "60x". help.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

16 Nov 2017, 01:05

2

abhishek94 wrote:

Bunuel wrote:

SOLUTION

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Given:

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) --> \(x=15\).

Answer: A.

Can you please explain "if x used both A and B, then 3x used only B (but not A).So, \(4x+140=200\) --> \(x=15\)" I can't comprehend this part. it is specifically mentioned in the question that 3 used 'only' brand B soap. So, why it is dependable on "both brands of soap" part. if so, why isn't 60 written as "60x". help.

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A).

So, for example: If 10 people used both brands of soap, 3*10 = 30 used only Brand B soap. If 12 people used both brands of soap, 3*12 = 36 used only Brand B soap. If x people used both brands of soap, 3x used only Brand B soap.
_________________

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

30 Sep 2018, 12:38

Bunuel wrote:

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Excellent opportunity to use Venn diagrams (a.k.a. "overlapping sets")!

\(? = x\)

\(120 = 60 + x + 3x\,\,\,\,\, \Rightarrow \,\,\,\,? = x = 15\)

Regards, Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

12 Feb 2019, 10:49

Solved this question algebraically as below:

Out of 200, 80 use none, so this leaves us with 120 using only A, only B and both. Only A users = 60, now this leaves us with Only B and both users to be remaining 60. Now, there's a relation given: 'for every household that used both brands of soap, 3 used only Brand B soap' this means both:only B = 1:3, assign x to 'both' users.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

04 May 2020, 21:12

1

Bunuel wrote:

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Diagnostic Test Question: 6 Page: 21 Difficulty: 650

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?

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

05 May 2020, 04:38

3

Asad wrote:

Bunuel wrote:

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Diagnostic Test Question: 6 Page: 21 Difficulty: 650

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Hello Asad,

You have asked a good question and a pertinent one too. Very often, in questions on Venn diagrams, the word “ONLY” can be the difference between a correct and a wrong answer. Let’s draw a Venn diagram to represent the situation defined in the question posed by you. It should look like this:

Attachment:

5th May 2020 - Reply 2.jpg [ 39.43 KiB | Viewed 3381 times ]

We see that x+y+z = 120 and x+z = 60. Therefore, y = 60 and z = 20 since \(\frac{z}{y}\) = \(\frac{1}{3}\).

The answer in this case would have been 20 i.e. option B. That should tell you that answer option B has been set up as a trap answer for students, who in their over-zealousness to get to the answer quickly may miss out the crucial keyword “only”.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
[#permalink]

Show Tags

05 May 2020, 14:34

Asad wrote:

Bunuel wrote:

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Diagnostic Test Question: 6 Page: 21 Difficulty: 650

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?

(A) 15 (B) 20 (C) 30 (D) 40 (E) 45

Hi Asad,

YES - if you edited the prompt in the way that you describe, then a change would occur in the Tic-Tac-Toe/Matrix Box that Bunuel presented. The "60" would appear in the lower-left corner of the grid, but the top row (re: X/3X/4X) would stay the same. You could then calculate the values of all of the boxes in the grid and the upper-left corner would be 20.