Question: 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

Answer: D

Solution and Explanation:

Approach Solution 1:

Given to us that

For every family that used both soap brands, three only used Brand B soap. This indicates that if a household used both A and B, then three only used B (but not A). As a result, 4x + 140 = 200,

x = 15

A is the correct answer.

Approach Solution 2:

Given that 80 houses do not use either Brand A or Brand B,
this means that 120 of the 200 households must use either Brand A, Brand B, or both.

Additionally, 60 households use only Brand A (which is correct), but three times as many uses both brands (WRONG? According to the data provided, just 3 people use Brand B)[/b].
3x homes use Brand B exclusively if x is the proportion of households using both Brand A and Brand B together. To see the logic of the data provided for this item, a Venn diagram can be useful:

Model A Model B
60 x 3 20 60 is provided. Given 3, 20 times 3 equals 60. However, if there are 120 users of Brand A (60) and B (3), only 57 users of Brand A & B remain after subtracting 120 - 60 - 3. This is how I initially saw the question, but since none of these solutions were viable, it seems logical to me that the proper response must be greater than 20.

After adding up and setting the value of 120 for all of the circle parts, the problem can be solved for x as follows:

60+x+3x=120
combine like phrases 60+4x=120
If 4x=60, take 60 off both sides.
x=15 divided by 4 on both sides

A is the correct answer.

“A marketing firm determined that, of 200 households surveyed, 80 used" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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