Problem Solving

akhp77 wrote:

mathewmithun wrote: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. What is the minimum possible value in percentage of the survey participants liked all three of the products.

ends up with the equation: II+2III=15 for which minimum possible value for III is 1. Correct?

Wrong.

Is it a trick question? The minimum is 0 (and the maximum is 7.5%)?

outreach wrote:The following equation can always be used for triple-overlapping set :

True # of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups)

or

True # of objects = (total in exactly 1 group) + (total in exactly 2 groups) + (total in exactly 3 groups)

mathewmithun wrote:I am bad in set, so can anyone explain how to approach such questions...thanks in advance...

Hi Outreach,

Thanks for your post.

Can n u pls explain the scenarioes when these two formulae need to be use??
Ur assistance would be much appreciated

Thanks
karthikd

In essence, you should remember only one formula to solve all kinds of set problems involving 3 sets,

Let there are 3 groups, A, B and C.

True # of items = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in at least 1/2) - (# in at least 1/3) - (# in at least 2/3) + (# in 1/2/3)

The confusion in this question is mainly due to things expresses as percentage terms. 85% is the total number surveyed and Product 1 is actually 50% of 85% of total term.

Open it up and put everything straight into realistic numbers and see how easily you can see the answer floating.

Check the attachment and let me know if any more doubt persists.

iikarthik wrote:

outreach wrote:The following equation can always be used for triple-overlapping set :

True # of objects = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in exactly 2 groups) - 2(# in all 3 groups)

or

True # of objects = (total in exactly 1 group) + (total in exactly 2 groups) + (total in exactly 3 groups)

mathewmithun wrote:I am bad in set, so can anyone explain how to approach such questions...thanks in advance...

Hi Outreach,

Thanks for your post.

Can n u pls explain the scenarioes when these two formulae need to be use??
Ur assistance would be much appreciated

Thanks
karthikd

For set problems such as these I encourage you to draw a Venn diagram so that you can see the situation visually. The Venn diagram can be adapted to almost any overlapping set question.

The big idea with overlapping sets is:

Subtract the overlap.

50 students study math
40 students study chemistry
10 students study both

The overlap is 10.
50-10 = 40 students who study ONLY math.
40-10 = 30 students who study ONLY chemistry.
50+40-10 = 80 total students (40 study only math, 30 study only chemistry, 10 study both).

With triple overlap questions, the easiest approach:

Subtract once the overlap of those in 2 groups (because they have been double-counted)
Subtract twice the overlap of those in all 3 groups (because they have been triple-counted)

Here's the formula:

Total = G(1) + G(2) + G(3) - (the number in exactly 2 groups) - 2*(the number in all 3 groups)

50 students study math
40 students study chemistry
20 students study art
10 students study 2 subjects
4 students study all 3 subjects

Total = 50+40+20-10-2*4 = 92 total students.

Hope this helps!

akhp77....

I am unable to find a result...can you please provide the result...