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

 It is currently 17 Oct 2019, 21:20

### 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

# A number of students from the same high school graduating class are en

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58408
A number of students from the same high school graduating class are en  [#permalink]

### Show Tags

20 Mar 2018, 00:58
00:00

Difficulty:

5% (low)

Question Stats:

92% (02:21) correct 8% (03:19) wrong based on 53 sessions

### HideShow timer Statistics

A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58408
Re: A number of students from the same high school graduating class are en  [#permalink]

### Show Tags

20 Mar 2018, 00:59
Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158

19. Overlapping Sets

For more:
ALL YOU NEED FOR QUANT ! ! !
_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
A number of students from the same high school graduating class are en  [#permalink]

### Show Tags

20 Mar 2018, 02:07
Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158

Given data:
P(M) = P(Ps) = 52
P(E) = 64
P(M U Ps) = 0
P(M U E) = 12
P(E U Ps) = 22

The maximum possible value of P(M U E U Ps) = 0 because we have
0 students who take both Mathematics and Psychology

P(Only M) = P(M) - {(P(M U E) + P(M U Ps)} = 52 - 12 = 40
P(Only E) = P(E) - {(P(M U E) + P(E U Ps)} = 64 - 34 = 30
P(Only Ps) = P(Ps) - {(P(E U Ps) + P(M U Ps)} = 52 - 22 = 30

Therefore, the total number of students who are in at least one course = $$40 + 30 + 30 +12 + 22$$ = 134(Option B)
_________________
You've got what it takes, but it will take everything you've got
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: A number of students from the same high school graduating class are en  [#permalink]

### Show Tags

20 Mar 2018, 02:30
1
Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158

I like to solve 3-overlapping sets problems with a diagram as it helps me visualize the data better.

Please find the image with solution.

Best,
Attachments

3-overlapping-sets.jpg [ 3.34 MiB | Viewed 829 times ]

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: A number of students from the same high school graduating class are en  [#permalink]

### Show Tags

21 Mar 2018, 16:14
Bunuel wrote:
A number of students from the same high school graduating class are enrolled at the same regional university in the fall semester. Of these students, 52 are enrolled in a mathematics course, 52 are enrolled in a psychology course, and 64 are enrolled in an English course. None of the students are enrolled in both mathematics and psychology. If 12 of the students are enrolled in both mathematics and English and 22 are enrolled in both psychology and English, how many of the students are in at least one of these three courses?

(A) 104
(B) 134
(C) 142
(D) 146
(E) 158

We can use the following equation:

#(at least one course) = #(M) + #(P) + #(E) - #(M & P) - #(M & E) - #(P & E) + #(M & P & E)

Since there are no students enrolled in both Mathematics and Psychology, #(M & P) = 0 and #(M & P & E)
= 0 and we have:

#(at least one course) = 52 + 52 + 64 - 0 - 12 - 22 + 0

#(at least one course) = 134

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 25 Mar 2016
Posts: 39
Location: India
Concentration: Finance, General Management
WE: Other (Other)
Re: A number of students from the same high school graduating class are en  [#permalink]

### Show Tags

22 Mar 2018, 10:44

considering number of student who enrolled for all 3 subject is zero and number of students enrolled for Mathematics & Psychology is zero (Given)
Re: A number of students from the same high school graduating class are en   [#permalink] 22 Mar 2018, 10:44
Display posts from previous: Sort by