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
Hello Experts,
EMPOWERgmatRichC,
VeritasKarishma,
IanStewart,
Bunuel,
chetan2u,
ArvindCrackVerbal,
GMATGuruNY,
AaronPond,
GMATinsightThe official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->
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 13088 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”.
Hope that helps!