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sets/venn diagram problem

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sets/venn diagram problem

by vzzai » Thu Nov 24, 2011 8:57 pm
There are 3 (A,B,C) selectors to select 30 people for a team. A selected 15 people, B selected 17 people, and C selected 20. What is the minimum number of people who are selected by ABC?
A, 0 B, 2 C, 3 D, 5 E, 10

Would I be able to use the following formula? Or should I use other method? Please explain
Total = A + B + C - (A&B) - (A&C) - (B&C) - 2(A&B&C)

Source: Some website...
Thank you,
Vj
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by user123321 » Fri Nov 25, 2011 6:39 am
vzzai wrote:There are 3 (A,B,C) selectors to select 30 people for a team. A selected 15 people, B selected 17 people, and C selected 20. What is the minimum number of people who are selected by ABC?
A, 0 B, 2 C, 3 D, 5 E, 10

Would I be able to use the following formula? Or should I use other method? Please explain
Total = A + B + C - (A&B) - (A&C) - (B&C) - 2(A&B&C)

Source: Some website...
is it A?

if we consider A,B and try to minimize then we will have at least two people who are selected by A&B.
now if we consider C, we can distribute those people into A & B without making above two people to be selected again.

edited:so, we can have A intersection B intersection C = 0, which is minimum


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Last edited by user123321 on Fri Nov 25, 2011 4:17 pm, edited 1 time in total.
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by shankar.ashwin » Fri Nov 25, 2011 7:14 am
Refer this post by Stuart

https://www.beatthegmat.com/least-value- ... tml#201338

But I am not sure if this problem is rightly framed for the answer choices dont match. Could you post the OA
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by vzzai » Fri Nov 25, 2011 7:48 am
I'm sorry, I don't have the OA.

AB + AC + BC + 2ABC = 22
and
AB + AC + BC + ABC = 30

This approach does not seem to be working here!
Thank you,
Vj
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by user123321 » Fri Nov 25, 2011 5:35 pm
It is a nice problem. It strengthened my understanding of sets.
I'm sorry, I don't have the OA.

AB + AC + BC + 2ABC = 22
and
AB + AC + BC + ABC = 30

This approach does not seem to be working here!
Actually you reached the solution.
But the mistake you did was assuming that A+B+C = 0
for now lets assume that we need to just think that A+B+C should be minimized.

Then actual equations are
AB + AC + BC + 2ABC = 22
A + B + C + AB + AC + BC + ABC = 30

eq 1 - eq 2 = ABC = A+B+C - 8
since we need to minimize A+B+C & maximize ABC & since we know that ABC can't be -ve
we can safely assume that A+B+C = 8
so ABC = 0

I can give an example of such a Venn diagram..

Image
hope this helps.

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by Stuart@KaplanGMAT » Sat Dec 03, 2011 9:02 pm
rethinking!
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by gunjan1208 » Fri Dec 09, 2011 5:53 am
15+17+20-2*30=-8

If the result is negative, minimum would be zero.
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