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There are a total of 400 students at a school, which offers a chorus, 22 Jan 2015, 07:39
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E
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There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130
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E
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BrentGMATPrepNow
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There are a total of 400 students at a school, which offers a chorus, 24 Nov 2018, 08:54
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Bunuel
There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

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The school offers a chorus, baseball, and Italian, and 15 students do all three activities
Draw 3 overlapping circles and start at the MIDDLE


Now we'll work from the middle to the outside.

40 students are in both chorus and Italian
So, 25 students must be in chorus and Italian, but not in baseball


45 students in both chorus & baseball
So, 30 students must be in chorus and baseball, but not in Italian


120 students are in the chorus
30 + 15 + 25 = 70
So, we've already accounted for 70 students in chorus.
So, the remaining 50 students must be in chorus ONLY


220 students are in either Italian or baseball
This is the trickiest part of the question.
This tells us that there are 220 students inside the two DARKENED circles below

As you can see, we've already accounted for 70 students inside the two DARKENED circles

So, the remaining 150 students are somewhere else inside the two DARKENED circles.

ASIDE: The precise location of those 150 doesn't matter, since the question doesn't specifically ask about this.

How many student are in none of the three activities?

At this point, the number of students we've accounted for = 50 + 30 + 15 + 25 + 150 = 270

There are 400 students in total.
So, the remaining 130 students must be OUTSIDE the circles.
On other words, 130 student are in none of the three activities

Answer: E

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There are a total of 400 students at a school, which offers a chorus, 28 Jan 2015, 01:26
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Answer = E. 130

Refer diagram below:

Attachment:
over.png
over.png [ 7.64 KiB | Viewed 21925 times ]
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There are a total of 400 students at a school, which offers a chorus, 22 Jan 2015, 23:38
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I used GmatClub formula

Total = A + B + C - (Sum of Overlaps) + All 3 + None

400 = 120 + 220 (either I or B) - ( 40 + 45 ) + 15 + None

I get None = 130

Is this appraoch correct?

I was confused with the foll stmnt
"If 220 students are in either Italian or baseball" .... but slotted this number in the above formula
Not 100% sure if this is correct
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There are a total of 400 students at a school, which offers a chorus, 28 Jan 2015, 01:28
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buddyisraelgmat
I used GmatClub formula

Total = A + B + C - (Sum of Overlaps) + All 3 + None

400 = 120 + 220 (either I or B) - ( 40 + 45 ) + 15 + None

I get None = 130

Is this appraoch correct?

I was confused with the foll stmnt
"If 220 students are in either Italian or baseball" .... but slotted this number in the above formula
Not 100% sure if this is correct
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That's correct. 220 is the complete pink shaded region a shown in figure above
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There are a total of 400 students at a school, which offers a chorus, 12 Mar 2015, 07:00
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Bunuel
There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

Kudos for a correct solution.
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MAGOOSH OFFICIAL SOLUTION:

This problem calls for a 3-way Venn Diagram. Here’s the diagram with no numbers filled in.
Attachment:
gpp-se_img13.png
gpp-se_img13.png [ 45.09 KiB | Viewed 21052 times ]
We know that C = 15. If 40 students are in both chorus & Italian, B + C = 40, and because C = 15, B = 25. If 45 students in both chorus & baseball, C + F = 45, and F = 30. We know that there are 120 in chorus, and B + C + F = 70, so E = 50.

Now, we are told that 220 student are in either Italian or baseball. Think about that region, Italian or baseball:
Attachment:
gpp-se_img14.png
gpp-se_img14.png [ 42.46 KiB | Viewed 20967 times ]
That entire purple region, A + B + C + D + F + G, is 220. If we add E = 50, that’s a total of 270 inside all three circles, which means that the outside of the circle, H, must equal 400 – 270 = 130.

Answer = (E).
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There are a total of 400 students at a school, which offers a chorus, 12 Apr 2015, 18:57
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Bunuel
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There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This problem calls for a 3-way Venn Diagram. Here’s the diagram with no numbers filled in.
Attachment:
gpp-se_img13.png
We know that C = 15. If 40 students are in both chorus & Italian, B + C = 40, and because C = 15, B = 25. If 45 students in both chorus & baseball, C + F = 45, and F = 30. We know that there are 120 in chorus, and B + C + F = 70, so E = 50.

Now, we are told that 220 student are in either Italian or baseball. Think about that region, Italian or baseball:
Attachment:
gpp-se_img14.png
That entire purple region, A + B + C + D + F + G, is 220. If we add E = 50, that’s a total of 270 inside all three circles, which means that the outside of the circle, H, must equal 400 – 270 = 130.

Answer = (E).
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You say "40 students in both chorus & Italian" --> Why do you take this as (B+C) ??? Shouldn't this be only B ?

The question explicitely states "15 students do all three activities" . That means the author of the question is telling us that he already seperated B and C! and C=15 ! and B=40 !



This question seems wrongly worded~

Please note the word "and" in the following sentence....

40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities

I think "and" implies that the numbers are in addition.. i,e you cannot say B+C is 40! It is actually B=40 and C=15...
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There are a total of 400 students at a school, which offers a chorus, 13 Sep 2018, 00:12
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buddyisraelgmat
I used GmatClub formula

Total = A + B + C - (Sum of Overlaps) + All 3 + None

400 = 120 + 220 (either I or B) - ( 40 + 45 ) + 15 + None

I get None = 130

Is this appraoch correct?

I was confused with the foll stmnt
"If 220 students are in either Italian or baseball" .... but slotted this number in the above formula
Not 100% sure if this is correct
Show more

Please correct me if I'm wrong but i don't think this is correct because you missed one overlap in your (Sum of Overlaps) which is the sum of 3 overlaps but only 2 are given in the question.
SO we have to do this by Venn Diagram.
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There are a total of 400 students at a school, which offers a chorus, 13 Sep 2018, 09:12
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Bunuel
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There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This problem calls for a 3-way Venn Diagram. Here’s the diagram with no numbers filled in.
Attachment:
gpp-se_img13.png
We know that C = 15. If 40 students are in both chorus & Italian, B + C = 40, and because C = 15, B = 25. If 45 students in both chorus & baseball, C + F = 45, and F = 30. We know that there are 120 in chorus, and B + C + F = 70, so E = 50.

Now, we are told that 220 student are in either Italian or baseball. Think about that region, Italian or baseball:
Attachment:
gpp-se_img14.png
That entire purple region, A + B + C + D + F + G, is 220. If we add E = 50, that’s a total of 270 inside all three circles, which means that the outside of the circle, H, must equal 400 – 270 = 130.

Answer = (E).
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Bunuel
The question says that 220 students are in either Italian or baseball. So, should our approach not be that A+B+C+D= 220 OR C+D+F+G= 220 ?
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There are a total of 400 students at a school, which offers a chorus, 24 Jan 2020, 10:19
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Bunuel
There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

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We can use the formula:

Total = n(C) + n(B) + n(I) – n(C and B) – n(C and I) – n(B and I) + n(C and B and I) + n(No Set)

Here we are given that Total = 400, n(C) = 120, n(C and I) = 40, n(C and B) = 45, n(C and B and I) = 15. We need to find n(No Set). We are not given n(B), n(I) and n(B and I). However, we are given that n(B or I) = 220. Recall that n(B or I) = n(B) + n(I) - n(B and I), so n(B) + n(I) - n(B and I) = 220.

We can rearrange the terms in our formula, substitute the numbers, and solve for n(No Set):

Total = n(C) – n(C and B) – n(C and I) + [n(B) + n(I) – n(B and I)] + n(C and B and I) + n(No Set)

400 = 120 - 45 - 40 + 220 + 15 + n(No Set)

400 = 270 + n(No Set)

130 = n(No Set)

Answer: E
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There are a total of 400 students at a school, which offers a chorus, 11 Jun 2020, 14:16
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Bunuel
There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

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Hi Guys, is there a way of solving this using a matrix?

If so, could someone describe it to me and solve the equation using a matrix?
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There are a total of 400 students at a school, which offers a chorus, 20 Jun 2021, 01:57
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Total - Neither = C + B + I + All 3 - (C and B) - (B and I) - (C and I)

=> 400 - Neither = 120 + B + I + 15 - 45 - (B and I) - 40

220 students are in either Italian or baseball: 220 = B + I - (B and I)

Therefore, 400 - Neither = 120 + 220 + 15 - 45 - 40

=> Neither = 400 - 270 = 130

Answer E
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There are a total of 400 students at a school, which offers a chorus, 12 May 2025, 02:46
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please specify formula for this
Bunuel
Bunuel
There are a total of 400 students at a school, which offers a chorus, baseball, and Italian. This year, 120 students are in the chorus, 40 students in both chorus & Italian, 45 students in both chorus & baseball, and 15 students do all three activities. If 220 students are in either Italian or baseball, then how many student are in none of the three activities?

A. 40
B. 60
C. 70
D. 100
E. 130

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

This problem calls for a 3-way Venn Diagram. Here’s the diagram with no numbers filled in.
Attachment:
gpp-se_img13.png
We know that C = 15. If 40 students are in both chorus & Italian, B + C = 40, and because C = 15, B = 25. If 45 students in both chorus & baseball, C + F = 45, and F = 30. We know that there are 120 in chorus, and B + C + F = 70, so E = 50.

Now, we are told that 220 student are in either Italian or baseball. Think about that region, Italian or baseball:
Attachment:
gpp-se_img14.png
That entire purple region, A + B + C + D + F + G, is 220. If we add E = 50, that’s a total of 270 inside all three circles, which means that the outside of the circle, H, must equal 400 – 270 = 130.

Answer = (E).
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