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Mugdho
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In a class of 100 students, 80 passed Physics, 70 passed Chemistry, an 21 Feb 2022, 05:08
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Skywalker18
Students that passed physics ,Set P=80
Students that passed chemistry , Set C = 70
Students that passed maths , Set M = 40

Students that failed all the 3 subjects = 10

Total = P + C + M - (PnC + CnM + PnM) + (PnCnM) + Neither
=>100 = 190 - (PnC + CnM + PnM) + (PnCnM) + 10
=> (PnCnM) = (PnC + CnM + PnM) - 100

For (PnCnM) to be minimum , (PnC + CnM + PnM) should be minimum .
So we need to the minimum overlap between the three sets.
For P and C ,
P=80
C=70
Then the total number of students that passed physcis and chemistry = 80+70 = 150
But there are only 90 students.
Therefore a minimum of 60 students passed physics and chemistry .
Similary for C and M ,
C+M=70+40=110
Therefore a minimum of 20 students passed Chemistry and Maths
And for P and M,
P+M=120
Therefore a minimum of 30 students passed Physics and Maths.
Mimimum value of (PnC + CnM + PnM) = 60+20+30=110

Minimum value of (PnCnM) = 110-100 =10

Answer C
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KarishmaB

is this solution correct? it’s saying "For (PnCnM) to be minimum , (PnC + CnM + PnM) should be minimum" which is opposite of urs.

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In a class of 100 students, 80 passed Physics, 70 passed Chemistry, an 21 Feb 2022, 23:40
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Mugdho
Skywalker18
Students that passed physics ,Set P=80
Students that passed chemistry , Set C = 70
Students that passed maths , Set M = 40

Students that failed all the 3 subjects = 10

Total = P + C + M - (PnC + CnM + PnM) + (PnCnM) + Neither
=>100 = 190 - (PnC + CnM + PnM) + (PnCnM) + 10
=> (PnCnM) = (PnC + CnM + PnM) - 100

For (PnCnM) to be minimum , (PnC + CnM + PnM) should be minimum .
So we need to the minimum overlap between the three sets.
For P and C ,
P=80
C=70
Then the total number of students that passed physcis and chemistry = 80+70 = 150
But there are only 90 students.
Therefore a minimum of 60 students passed physics and chemistry .
Similary for C and M ,
C+M=70+40=110
Therefore a minimum of 20 students passed Chemistry and Maths
And for P and M,
P+M=120
Therefore a minimum of 30 students passed Physics and Maths.
Mimimum value of (PnC + CnM + PnM) = 60+20+30=110

Minimum value of (PnCnM) = 110-100 =10

Answer C

KarishmaB

is this solution correct? it’s saying "For (PnCnM) to be minimum , (PnC + CnM + PnM) should be minimum" which is opposite of urs.

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Both are correct and both are different formats.

I like to think in terms of people and instances (say every pass is a card with "pass" written on it), I have to distribute 190 of these cards among 90 students. So I give away 90 cards so each student has a pass. Of the other 100, if I want to minimise the overlap of all 3, I give in such a way that maximum students get 2 cards so I give another 1 card to all 90 student. But I still have 10 leftover so an overlap of 10 for all 3 is essential.

In the solution above:
(PnCnM) = (PnC + CnM + PnM) - 100

Note that
(PnC + CnM + PnM) = (Only P&C + All 3) + (Only C&M + All 3) + (Only P&M + All 3)
(PnC + CnM + PnM) = (Only 2) + 3 * (All 3)

So
All 3 = (PnC + CnM + PnM) - 100
becomes
(All 3) = (Only 2) + 3 * (All 3) - 100
100 = (Only 2) + 2 * (All 3)

Now if I want to minimise (All 3), I must maximise (Only 2) and that is what I do using the instances logic.
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In a class of 100 students, 80 passed Physics, 70 passed Chemistry, an 22 Feb 2022, 22:32
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Mugdho
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Bunuel

Jamboree and GMAT Club Contest Starts




QUESTION #13:

In a class of 100 students, 80 passed Physics, 70 passed Chemistry, and 40 passed Math. If 10 students failed in all the three subjects, at least how many of the students passed all the three subjects?

(A) 0
(B) 5
(C) 10
(D) 20
(E) 25


Check conditions below:


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For the following two weekends we'll be publishing 4 FRESH math questions and 4 FRESH verbal questions per weekend.

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, respective forum moderators will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize. He/She can opt for one of the following as a Grand Prize. It will be a choice for the winner:
-- GMAT Online Comprehensive (If the student wants an online GMAT preparation course)
-- GMAT Classroom Program (Only if he/she has a Jamboree center nearby and is willing to join the classroom program)

Bookmark this post to come back to this discussion for the question links - there will be 2 on Saturday and 2 on Sunday!



There is only one Grand prize and student can choose out of the above mentioned too options as per the conditions mentioned in blue font.
All announcements and winnings are final and no whining :-) GMAT Club reserves the rights to modify the terms of this offer at any time.

NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!


Answer: option C

Detailed explanation is as follows


GMATinsight
Can u tell me plz how did u get the first line 2(a+b+c)+d+e+f=80?

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Outside variables of circle of 40
a+b+e = 100-10-40= 50

Similarly
a+d+c = 100-70-10 = 20

Similarly,
b+c+f = 100-80-10 = 10

Add these three equations.

2(a+b+c)+d+e+f=80

I hope this help

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In a class of 100 students, 80 passed Physics, 70 passed Chemistry, an 20 Jul 2025, 12:22
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