Problem Solving

Stmt 150% of those asked liked product 1

Stmt 250% of those asked liked product 1 only

what percentage of the survey participants liked more than one of the three products?

Here it is:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither


But i am still not able to apply it , i am posting two problems, If those problems can be solved using the above formula , kindly explain in detail.

Q1 :
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

Q2 :
There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.

crejoc wrote:The Three Overlapping Sets Formula

Here it is:
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither


By my terminology
Group1= All those people who like 1
Group1=A+x+y+z
A= Like Only 1
x= like 1 and 2
y= like 1 and 3
z= like 1,2 and 3

Group2= B+x+v+z
B= Like Only 2
v= like 2 and 3

Group3=C+y+v+z
C= Like Only 3

Also x+y+v+z= People who like more than one

A+B+C= People who like EXACTLY ONE product

x+y+v= People who like EXACTLY TWO product


According to Question 1 you have to find x+y+v+z

You are given
Group1=50%
Group2=30%
Group3=20%
All three(z)=5%

Also people who do not like any of the three products=(100-85)%
=>Neither=15% in your formula

As you can see for yourself the equation that you have given will yield

sum of 2 group overlap=x+y+v
you already know All three(z)=5%

hence you can find the answer. I HOPE You UNDERSTAND



What i wanted to emphasize was, USE the formula only when you understand what really comprises Group1,Group2,Group3

Q1 :
In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?

Stuart Kovinsky wrote:

Q1:

100 = 50 + 30 + 20 - (people who like 2 products) - 2(5) + 15

(Since it's a percent question, just let total number = 100.)



Q2 :

70 = 40 + 30 + 35 - (exactly 2 courses) - 2(15) + 0

(All 70 are in one of the subjects, so "none" = 0.)

Thank you so much , i could understand clearly now, thanks a lot.

rah_pandey wrote:
By my terminology
Group1= All those people who like 1
Group1=A+x+y+z
A= Like Only 1
x= like 1 and 2
y= like 1 and 3
z= like 1,2 and 3

Group2= B+x+v+z
B= Like Only 2
v= like 2 and 3

Group3=C+y+v+z
C= Like Only 3