Bunuel wrote:
violetsplash wrote:
A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below
48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food
What is the number of students who like none or only one of the foods ?
A. 4
B. 16
C. 17
D. 20
E. 23
I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way.
\(Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither\).
75 = 48 + 45 + 58 - (28 + 37 + 40) + 25 + Neither --> Neither = 4.
Only Pizza = P - (P and H + P and T - All 3) = 48 - (28 + 40 - 25) = 5;
Only Hoagies = H - (P and H + H and T - All 3) = 45 - (28 + 37 - 25) = 5;
Only Tacos = T - (P and T + H and T - All 3) = 58 - (40 + 37 - 25) = 6.
The number of students who like none or only one of the foods = 4 + (5 + 5 + 6) = 20.
Answer: D.
For more check ADVANCED OVERLAPPING SETS PROBLEMS:
http://gmatclub.com/forum/advanced-over ... 44260.htmlHope this helps.
Hi Bunuel request you to assist me
Only Pizza = P - (P and H + P and T - All 3) = 48 - (28 + 40 - 25) = 5;
While solving for Only one food.
If 28 (Pizza and Hoagies) Includes the G part i.e all three
and 40 (Pizza and Tacos) also includes the G part
Aren't we adding G 2 times and subtracting only once?
To further simply my query:
in the question it says 28 people like pizza and hoagies; however, the 28 people also include people who like pizza, hoagies AND tacos. Similarly for 40 question says 40 like Pizza and Hoagies; however, the 40 also includes people who like tacos.
When we add the two, i.e P and H + P and T don't we end up adding all three portion twice and subtract it only once?
Please help