GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 May 2019, 20:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55150
There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

22 Jan 2015, 07:39
4
16
00:00

Difficulty:

75% (hard)

Question Stats:

60% (02:51) correct 40% (03:18) wrong based on 314 sessions

### HideShow timer Statistics

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.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

28 Jan 2015, 01:26
6
1

Refer diagram below:

Attachment:

over.png [ 7.64 KiB | Viewed 4453 times ]

_________________
Kindly press "+1 Kudos" to appreciate
##### General Discussion
Manager
Joined: 14 Jul 2014
Posts: 91
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

22 Jan 2015, 23:38
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
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

28 Jan 2015, 01:28
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
_________________
Kindly press "+1 Kudos" to appreciate
Math Expert
Joined: 02 Sep 2009
Posts: 55150
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

12 Mar 2015, 07:00
2
2
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 [ 45.09 KiB | Viewed 4246 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 [ 42.46 KiB | Viewed 4249 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.

_________________
Manager
Status: Manager to Damager!
Affiliations: MBA
Joined: 22 May 2014
Posts: 61
Location: United States
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

12 Apr 2015, 18:57
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.

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...
Intern
Joined: 07 Jul 2018
Posts: 47
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

13 Sep 2018, 00:12
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.
Intern
Joined: 16 Jul 2017
Posts: 23
Location: India
Concentration: Finance, Economics
There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

13 Sep 2018, 09:12
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.

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 ?
CEO
Joined: 12 Sep 2015
Posts: 3716
Re: There are a total of 400 students at a school, which offers a chorus,  [#permalink]

### Show Tags

24 Nov 2018, 08:54
1
Top Contributor
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.

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.

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

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Re: There are a total of 400 students at a school, which offers a chorus,   [#permalink] 24 Nov 2018, 08:54
Display posts from previous: Sort by