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There are 500 students in a class. 450 of them take Course A, 300 of t
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26 Jun 2021, 18:56

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Question Stats:

There are 500 students in a class. 450 of them take Course A, 300 of them take Course B, and 150 of them take Course C. Each student has to take at least one course, and 100 of them take all the three classes simultaneously. The number of students who take both Course A and Course B, but not Course C could be?

Indicate all such possible values.

A. 50

B. 100

C. 150

D. 200

E. 250

Post a detailed solution and get kudos!

_________________

Indicate all such possible values.

A. 50

B. 100

C. 150

D. 200

E. 250

Post a detailed solution and get kudos!

_________________

PhD in Applied Physics

Re: There are 500 students in a class. 450 of them take Course A, 300 of t
[#permalink]
26 Jun 2021, 23:58

1

At the beginning 450 + 300 + 150 = 900

people who have chosen 100 in all three courses. Explain that 100 people have been counted three times.

900-200 = 700

700-500 = 200. For the number of double-choices,

we get the upper limit of 200 people. Now look for the lower limit

C and remove it. Three choices of people, 150-100 = 50 BC + AC up to 50 people, then the remaining 200 -50 must be filled by AB, that is, at least 150

, the range of possibilities is 150 to 200

Answer: C & D

Posted from my mobile device

people who have chosen 100 in all three courses. Explain that 100 people have been counted three times.

900-200 = 700

700-500 = 200. For the number of double-choices,

we get the upper limit of 200 people. Now look for the lower limit

C and remove it. Three choices of people, 150-100 = 50 BC + AC up to 50 people, then the remaining 200 -50 must be filled by AB, that is, at least 150

, the range of possibilities is 150 to 200

Answer: C & D

Posted from my mobile device

Re: There are 500 students in a class. 450 of them take Course A, 300 of t
[#permalink]
27 Jun 2021, 02:29

another explanation for above question please

Retired Moderator

Joined: **09 Jan 2021 **

Posts: **576**

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There are 500 students in a class. 450 of them take Course A, 300 of t
[#permalink]
27 Jun 2021, 03:38

1

void wrote:

another explanation for above question please

Hi There!

Let me try helping you!

Students who study course A (This includes only A, A& B, A& C & A,B & C)=450

Students who study course B= 300

Students who study course=150

Now, as we know the 100 students who study all the 3 subjects will be included in the above students and they will be counted thrice i.e. once in A, B & C. Therefore we can subtract this from all the three

A(This includes only A, A& B, A& C )450-100=350

B=300-100=200

C=150-100=50

Now the above values are those values which includes individual and two courses together.

Total students=500

350+200+50+100=700

700-500=200

Thus, there has to be 200 students combined (A& B, B& C, A& C)

As we know that C has only 50 students left the maximum it can share with A & B is 50

So, If A& C or B& C= 50. The left 150 has to be filled by A & B to give us a total of 500.

And if those 50 take up only C course. Then 200 students take A& B together.

IMO C & D

Hope this helps!

Capture.PNG [ 31.5 KiB | Viewed 4489 times ]

Retired Moderator

Joined: **16 Apr 2020 **

Status:**Founder & Quant Trainer**

Affiliations: **Prepster Education**

Posts: **1546**

Location: **India**

WE:**Education (Education)**

Re: There are 500 students in a class. 450 of them take Course A, 300 of t
[#permalink]
27 Jun 2021, 03:45

1

kumarneupane4344 wrote:

There are 500 students in a class. 450 of them take Course A, 300 of them take Course B, and 150 of them take Course C. Each student has to take at least one course, and 100 of them take all the three classes simultaneously. The number of students who take both Course A and Course B, but not Course C could be?

Indicate all such possible values.

A. 50

B. 100

C. 150

D. 200

E. 250

Post a detailed solution and get kudos!

Indicate all such possible values.

A. 50

B. 100

C. 150

D. 200

E. 250

Post a detailed solution and get kudos!

AUBUC + Leftovers= A + B + C - (d + e + f) - 2(A∩B∩C)

500 + 0 = 450 + 300 + 150 - (d + e + f) - 2(100)

(d + e + f) = 200

For Maximization;

e = f = 0

i.e. d = 200

For Minimization;

As, C = f + e + 100

150 = e + f + 100

e + f = 50

Therefore, d + 50 = 200

i.e. d = 150

Hence, option C and D

There are 500 students in a class.png [ 19.52 KiB | Viewed 4509 times ]

_________________

I hope this helps!

Regards:

Karun Mendiratta

Founder and Quant Trainer

Prepster Education, Delhi, India

https://www.instagram.com/prepster_education/

Regards:

Karun Mendiratta

Founder and Quant Trainer

Prepster Education, Delhi, India

https://www.instagram.com/prepster_education/

Re: There are 500 students in a class. 450 of them take Course A, 300 of t
[#permalink]
03 Dec 2023, 15:09

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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