saintforlife
Solution:
I don't like drawing Venn diagrams because it is time consuming. I tend to use the formula:
(Total in Group 1) + (Total in Group 2) + (Total in Group 3) – (Overlap of 1 and 2) – (Overlap of 1 and 3) – (Overlap of 2 and 3) – [2 * (Overlap of 1, 2, and 3)] + (total in none of the groups) = Overall total
10 + 20 + 18 - 5 - 3 - 4 - 2(x) + 0 = 38.
=> 48 - 12 - 2x = 38
=> 36 - 2x = 38
=> x=-1
But the answer is:
X = 2
Where am I going wrong? I used the method suggested by Bunuel in this thread:
gmatclub dot com/forum/at-a-certain-resort-each-of-the-39-food-service-employees-133276.html
I agree that drawing venn diagram is a time taking thing. But you should be able to picturize the venn diagram in your mind to correctly understand the problem
As shown in the venn diagram below:
Attachment:
Venn_Diagram.png [ 14.39 KiB | Viewed 18785 times ]
a = only action
b = only drama
c= only comedy
d = both action and drama but not comedy
e = both action and comedy but not drama
f = both drama and comedy but not action
g = all three
As per the question,
Both action and drama (including comedy) = d + g = 5
Both action and comedy (including drama) = e + g = 3
Both drama and comedy (including action) = f + g = 4
Action = a + d + g + e = 10
Drama = b + d + f + g = 20
Comedy = c + e + f + g = 18
As per your formula:
(Total in Action) + (Total in Drama) + (Total in Comedy) – (Overlap of A and D) – (Overlap of D and C) – (Overlap of A and C) – [2 * (Overlap of A, D, and C)] + (total in none of the groups) = Overall total
=> (a + d +
g + e) + (b + d + f +
g) + (c + e + f +
g) – (d +
g) – (e +
g) – (f +
g) – (2*
g) + 0 = 38
Here you can see that you are adding
g thrice but subtraction
g 5 times (3 + 2)
So instead of subtracting 2g, you have to add “g” once as you have already added g thrice and subtracted thrice earlier
Hence the correct formula should be:
(a + d +
g + e) + (b + d + f +
g) + (c + e + f +
g) – (d +
g) – (e +
g) – (f +
g)
+ (
g) + 0 = 38
=> 10 + 20 + 18 - 5 - 3 – 4 + g = 38
=> 48 – 12 + g = 38
=> 36 + g = 38
=> g = 38 – 36 = 2