Last visit was: 25 Apr 2026, 04:01 It is currently 25 Apr 2026, 04:01
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
gmat_crack
User avatar
Joined: 22 Nov 2005
Last visit: 04 Aug 2009
Posts: 209
Own Kudos:
71
Posts: 209
Kudos: 71
Three teachers test 30 students. A agrees 15 students can 28 May 2006, 18:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
Three teachers test 30 students. A agrees 15 students can pass the test, B agrees 7 students can pass the test, and C agrees 24 students can pass the test. With both three teachers’ agreement, a student can pass the test. At least how many students can pass the test?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
Professor
User avatar
Joined: 29 Dec 2005
Last visit: 09 Aug 2011
Posts: 562
Own Kudos:
184
Posts: 562
Kudos: 184
Three teachers test 30 students. A agrees 15 students can 28 May 2006, 20:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmat_crack
Three teachers test 30 students. A agrees 15 students can pass the test, B agrees 7 students can pass the test, and C agrees 24 students can pass the test. With both three teachers’ agreement, a student can pass the test. At least how many students can pass the test?
Show more


max = 7
minimum/at least = 0, if i am not missing anything....
User avatar
ywilfred
User avatar
Joined: 07 Jul 2004
Last visit: 06 Mar 2012
Posts: 1,987
Own Kudos:
2,051
Location: Singapore
Posts: 1,987
Kudos: 2,051
Three teachers test 30 students. A agrees 15 students can 28 May 2006, 22:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We have

#(all three agree) = 1
#(A and B agree) = x
#(A and C agree) = y
#(B and C agree) = z
#(A only) = 15-x-y-1 = 14-x-y
#(B only) = 7-x-z-1 = 6-x-z
#(C only) = 24-z-y-1 = 23-z-y
#(none) = n

So 1 + x + Y + z + 14-x-y + 6-x-z + 23-z-y + n = 30
44-x-y-z= 30
x+y+z= 14

I assume to pass the test, you need at least two teacher's agreement (majority rule). So at least 15 students will pass the test.
avatar
Gambler007
avatar
Joined: 22 May 2006
Last visit: 01 Jun 2006
Posts: 1
Posts: 1
Kudos: 0
Three teachers test 30 students. A agrees 15 students can 30 May 2006, 05:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From ven dia (file attached)

I - sum of students that individual teachers (A/B/C) agree will pass

I = Ia + Ib + Ic

II - sum of students that any 2 teachers agree will pass

II = IIab + IIbc + IIac

III - all 3 teachers agree student will pass

Note: our ans is to find min III.

we can say

I + II + III = 30 (total no of stucents) ..........(1)

if we add no of students that will be passed by individual teahcer

15 = Ia + IIab + IIbc + IIIabc

7 = Ib + IIbc + IIba + IIIabc

24 = Ic + IIca + IIbc + IIIabc

Now I = Ia + Ib + Ic

II = IIab + IIbc + IIca

hence we can say

15 + 7 + 24 = I + 2II + 3III

I + 2II + 3III = 46............(2)

subtract (2) - (1)

II + 2III = 16

for min III, III can be zero

for max III, II = 0

hence 2 III = 16 -->> III = 8

hence no of students atleast passed = 0 and maximum students passed (as per q) can be 8.


[/img]
User avatar
tl372
User avatar
Joined: 10 May 2006
Last visit: 16 Jul 2013
Posts: 100
Own Kudos:
10
Location: USA
Posts: 100
Kudos: 10
Three teachers test 30 students. A agrees 15 students can 30 May 2006, 11:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Minimum - 0
Max - 7

Explanations:

MIN - The minimum would be where the 3 teaches have the least amount of overlap. If you imagine a number line with all 30 kids lined up in a row labelled #1 - #30:

Teacher C's students (24) = Student #1-#24
Teacher B's students (7) = Student #24-#30 *one overlap with C
Teacher A's students (15) = Student #1 - 15

Teacher A will have all 15 students overlapping with C, and none with B. As you can see, there are no students that have all 3 teacher's endorsement.

MAX - You want to maximize the amount of overlap between the teachers.

Teacher C - Student #1 - #24
Teacher B - Student #1 - #7
Teacher A - Student #1 - #15

There are 7 kids total who have an endorsement from all three teachers. In essence, for the max number, just take the # of students from the teacher with the fewest (teacher B).



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
109822 posts