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

This topic has expert replies

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: 28 Dec 2011
Location: Berkeley, CA
Thanked: 387 times
Followed by:140 members
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


For a discussion of set problem such as this, as well as the OA & OE of this particular question, please see:
https://magoosh.com/gmat/2014/gmat-prac ... lems-sets/

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/

Senior | Next Rank: 100 Posts
Posts: 37
Joined: 10 Mar 2010
Thanked: 4 times
GMAT Score:700

by nipunranjan » Fri Oct 24, 2014 11:18 am
(E)

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 15463
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1266 members
GMAT Score:770
[email protected] wrote:
Mon Oct 20, 2014 10:45 am
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

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

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
Image

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

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
Image

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
Image
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.
Image
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?
Image
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

Cheers,
Brent
Image

A focused approach to GMAT mastery

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 6195
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:24 members
[email protected] wrote:
Mon Oct 20, 2014 10:45 am
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


For a discussion of set problem such as this, as well as the OA & OE of this particular question, please see:
https://magoosh.com/gmat/2014/gmat-prac ... lems-sets/

Mike :-)
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage