Hi
I have not been able to understand question 6 of the Quantitative section explanation at page 48.
Question 6 explanation: Arithmetic operations on rational numbers NOTE I copied exactly how GMAT written the question and explanation[/b]
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
[Their explanation]
Since it is given that 80 households use neither Brand A nor Brand B, then 200-80 = 120
(UNTIL HERE IT IS CORRECT) must use Brand A, Brand B, or both.
It is also given that 60 households use only Brand A [b](CORRECT) and that three times as many households use both brands
(WRONG? IN THE DATA GIVEN IT SAYS ONLY 3 PEOPLE USE BRAND B) [/b]. If x is the number of households that use both Brand A and Brand B, then 3x use Brand B alone. A Venn diagram can be helpful for visualizing the logic of the given information for this item:
Brand A Brand B
60 x 3x
(I HAD ANSWER B. 20 60 is given 3 is given so 20 times 3 = 60 However, if we have 120 people who used Brand A (60) and B (3) than subtract 120 - 60 - 3 = 57 is left so they must use both Brand A & B. This is how I at first saw it but since non of these answers were possible it only makes sense to me the correct answer must be than 20)All the sections in the circles can be added up and set equal to 120, and then the equation can be solved for x:
60+x+3x=120
60+4x=120 combine like terms
(WHERE DOES THE 4 COMES FROM)4x=60 subtract 60 from both sides
x=15 divided both sides by 4
Answer A
please explain to me if I am wrong. I will post more mistakes I have noticed in the book.thanks
TD