M03-07

I think this question is good and helpful.

I think this is a high-quality question and I don't agree with the explanation. I think the answer is 55%.
n(AUBUC) = n(A) + n(B) + n(C) -n(AnB)-n(BnC)-n(CnA) + n(AnBnC)
Thus
100 = 60+50+35 -x +10
Therefore, x = 55%
Alternate,
through venn diagram,
if n(AnB) = x; n(BnC) = y; n(CnA) = z
then adding each one individually;
[60-x-(y-10)+50-x-(z-10)+35-z-(y-10)] + [x-10+y-10+z-10]+ [10] = 100
will result in x+y+z = 55%

The formula you are using is not correct. It should be:

{Total} = {Group 1} + {Group 2} + {Group 3} - {those in 2 of the groups} - 2*{those in all 3 groups}

Could you explain why we multiply the last part by two please? I can't get the logic behind that

Check ADVANCED OVERLAPPING SETS PROBLEMS

Also check:

• Overlapping Sets Made Easy!
• How to draw a Venn Diagram
• Data Sufficiency Questions on Overlapping Sets
• Problem Solving Questions on Overlapping Sets

Great! Thank you Bunuel. I really need to learn my way through this website. So many useful materials.

I think this is a high-quality question and I agree with explanation.

I solved it slightly differently and find this approach more intuitive than applying a specific formula (mind you got it right at the third try but that is just on my carelessness). Hope this helps:

With questions like these, I find it useful to make a Venn Diagram to help in visualizing and summarizing all the data.

So we are given the info represented in the Venn Diagram, and we are also told that all customers buy AT LEAST one of the three items, so we know that the three should sum up to 100. Further the deductions are just the customers who buy a combination of any two of the three items or all three items in case of the 10 from each of the three items.

Given all this info all we need to do now is to simply add up all these terms and find the value of x + y + z , which represents the proportion of customers that but exactly two of the three items.

So we have the equation:

[60 - x - y -10] + [35 - x - z - 10] + [50 - y - z - 10] + x + y + z + 10 = 100

i.e. [proportion of those that buy only milk] + [proportion of those that buy only apples] + [proportion of those that only buy chicken] + customers that buy milk and apples + those that buy milk and chicken + those that buy chicken and apples + those that buy all three = 100 (because all %ages of customers surveyed should total 100)

When you simplify the above expression you will eventually arrive at:

x + y + z = 25

The answer is thus D

I know it seems a bit long winded but for me it is the most intuitive way of solving the problem.

I think this is a high-quality question and I agree with explanation.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

I like the solution - it’s helpful.