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There are a total of 400 students at a school, which offers a chorus,

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There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 22 Jan 2015, 06:39
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  75% (hard)

Question Stats:

62% (02:52) correct 38% (03:26) wrong based on 229 sessions

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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.

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Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 28 Jan 2015, 00:26
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Answer = E. 130

Refer diagram below:

Attachment:
over.png
over.png [ 7.64 KiB | Viewed 3560 times ]

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Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 22 Jan 2015, 22:38
1
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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Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 28 Jan 2015, 00:28
buddyisraelgmat wrote:
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


That's correct. 220 is the complete pink shaded region a shown in figure above
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Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 12 Mar 2015, 06:00
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Bunuel wrote:
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
gpp-se_img13.png [ 45.09 KiB | Viewed 3356 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 3358 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 12 Apr 2015, 17:57
Bunuel wrote:
Bunuel wrote:
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).







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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Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

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New post 12 Sep 2018, 23:12
buddyisraelgmat wrote:
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


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,  [#permalink]

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New post 13 Sep 2018, 08:12
Bunuel wrote:
Bunuel wrote:
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).


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, &nbs [#permalink] 13 Sep 2018, 08:12
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