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Dear Bunuel,
huge thanks for this post:
I'm trying to find difference between two given formulas in order to apply them correctly.

Am I right to say that formula #1 applicable to GENERAL CASES
FIRST FORMULA

$$Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither$$.

while formula#2 might be used ONLY when in premise says something as belong/ include ONLY to two groups/categories?
SECOND FORMULA

$$Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither$$.

Thanks a lot for help-you are my hero!
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3111987 wrote:
Dear Bunuel,
huge thanks for this post:
I'm trying to find difference between two given formulas in order to apply them correctly.

Am I right to say that formula #1 applicable to GENERAL CASES
FIRST FORMULA

$$Total = A + B + C - (sum \ of \ 2-group \ overlaps) + (all \ three) + Neither$$.

while formula#2 might be used ONLY when in premise says something as belong/ include ONLY to two groups/categories?
SECOND FORMULA

$$Total = A + B + C - (sum \ of \ EXACTLY \ 2-group \ overlaps) - 2*(all \ three) + Neither$$.

Thanks a lot for help-you are my hero!

Yes, you can generalize this way. Check examples in my post to verify.
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Signed up just to comment.

Flawless. Works like a charm. Too good to be true!!!

Posted from my mobile device
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asagraw wrote:
Hi Bunuel,

I am not able to understand first formula. As you mentioned "When we add three groups A, B, and C some sections are counted more than once. For instance: sections d, e, and f are counted twice and section g thrice." but aren't we counting g six times? Please explain as I am very much confused with this. Thanks.

Regards,
Ashish

Why is g counted 6 times?

Each of A, B, and C contains one g. When we sum, g is counted thrice.
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Great material. I guess it can solve one of the hardest 3 overlapping sets . I knew the Formula 2 but I never knew the detail application and tried to apply on the one which needs Formula 1 ...wasted lot of time on practice exam ... Now i guess I will be able to distinguish them .

Also I guess for problems with 2 sets , Matrix methods is best and can solve any problem. For 3 its become little problematic.

Regards.
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Great post! Thank You Bunuel.
A minor typo:
Q 6 has
"E and M had 9 names in common, E and S had 7, and M and S had 10": EnM=19, EnS=7, and MnS=10;

I believe, it should be
"E and M had 9 names in common, E and S had 7, and M and S had 10": EnM=9, EnS=7, and MnS=10;
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Hi Bunuel,
Thanks a ton for this post. Really helped me clear my mind of useless assumptions.
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Thanks Bunuel for sharing this. +1 Kudos!!!

The two formulas are really helpful and work each and every time.

As mentioned by others, it took some time for me to understand both the formulas. So, I kind of tried to write the formula a way for my better understanding. Attaching a screenshot for the same. Hope this might be helpful for others.
Attachments

overlappingSet.jpg [ 464.59 KiB | Viewed 43475 times ]

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Bunuel
Thanks for this, Bunuel! Truly appreciate it.
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Bunuel : awesome Post Sir !!

although i uderstood it , Can you make a video on this formula derivation.

I know , its too much to ask , still Sir, whenever you have spare time,

Thanks
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This is so brilliant. Cleared all my doubts on when to use which formula. Hopefully I'll be able to retain them and not get confused.
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Thanks a lot Bunuel. I wish I could give you 100 kudos at once
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This post is amazing.Thanks
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Bunuel wrote:
Example 10 (hard DS question on three overlapping sets):
A student has decided to take GMAT and TOEFL examinations, for which he has allocated a certain number of days for preparation. On any given day, he does not prepare for both GMAT and TOEFL. How many days did he allocate for the preparation?

(1) He did not prepare for GMAT on 10 days and for TOEFL on 12 days.
(2) He prepared for either GMAT or TOEFL on 14 days

Fantastic post with some really great examples, Bunuel!
But isn't example 10 a question with two overlapping sets? I found using the double matrix for this example work out perfectly, and in a more preferable way personally. (see photo)
What makes it have three overlapping sets? Is there a particular reason why you look at this kind of a question as having three overlapping sets?
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Bilde1.png [ 27.52 KiB | Viewed 31499 times ]

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