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Re: There are 230 students at Augustus Middle School. 80 of those students [#permalink]
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Bunuel wrote:
There are 230 students at Augustus Middle School. 80 of those students play football, 42 play soccer and 12 play rugby. 32 students play exactly two of the sports, and only 4 students play all three of the sports. How many of the students at Augustus Middle School play none of the three sports?

A. 94
B. 115
C. 132
D. 136
E. 140


Solution:

We can use the formula:

Total = n(A) + n(B) + n(C) – n(exactly two sets) - 2 * n(all 3 sets) + n(no set)

230 = 80 + 42 + 12 - 32 - 2 * 4 + n(no set)

230 = 94 + n(no set)

136 = n(no set)

Answer: D
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Re: There are 230 students at Augustus Middle School. 80 of those students [#permalink]
Hello,

the formula method makes such problems quite easy, however I get mixed up on when to add the multiplication of "2X" for the set of 3.

Some problems(Below the first sentence of the problem, I was not able to add a hyperlink) that ask for the set of 3 don't add the "2X" while the one above as it used.
"The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy."

Appreciate your elaboration on this, thanks!
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Re: There are 230 students at Augustus Middle School. 80 of those students [#permalink]
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abdullaelmasri wrote:
Hello,

the formula method makes such problems quite easy, however I get mixed up on when to add the multiplication of "2X" for the set of 3.

Some problems(Below the first sentence of the problem, I was not able to add a hyperlink) that ask for the set of 3 don't add the "2X" while the one above as it used.
"The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy."

Appreciate your elaboration on this, thanks!


You see there are two different formulae for 3 overlapping sets. One has +(all three) and another has -2(all three).

Check this topic: ADVANCED OVERLAPPING SETS PROBLEMS, it explains the logic behind the formulae in detail.

Hope it helps.
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Re: There are 230 students at Augustus Middle School. 80 of those students [#permalink]
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