Club Number of Students
Chess 40
Drama 30
Math 25
The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?
(A) 68
(B) 69
(C) 74
(D) 79
(E) 84
Cannot get a proper solution for this one
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One formula for 3 overlapping groups:Architj wrote:Club Number of Students
Chess 40
Drama 30
Math 25
The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?
(A) 68
(B) 69
(C) 74
(D) 79
(E) 84
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of the groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let total = T.
Chess = 40.
Drama = 30.
Math = 25.
Exactly 2 of the groups = 10+5+6.
All 3 groups = 0.
Plugging these values into the formula, we get:
T = 40 + 30 + 25 - (10+5+6) - 2*0
T = 74.
The correct answer is C.
Similar problem:
https://www.beatthegmat.com/og-13-178-vi ... 11188.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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