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If the Number of students learning exactly two subjects is maximum and

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If the Number of students learning exactly two subjects is maximum and  [#permalink]

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New post 01 Nov 2019, 06:31
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The Number of students learning three subjects are as follows

Maths = 40
English = 50
Science = 35

If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?

A. 0
B. 1
C. 25
D. 35
E. 45


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Re: If the Number of students learning exactly two subjects is maximum and  [#permalink]

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New post 01 Nov 2019, 13:11
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'


we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62



Bunuel wrote:
The Number of students learning three subjects are as follows

Maths = 40
English = 50
Science = 35

If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?

A. 0
B. 1
C. 25
D. 35
E. 45


Are You Up For the Challenge: 700 Level Questions

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Re: If the Number of students learning exactly two subjects is maximum and  [#permalink]

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New post 02 Nov 2019, 03:34
total = M+E+S-2*all subjects
total = 40+50+35-2x
total = 125-2x
value will be minimized at value of x = 62 ; ie we then get = 125-124 ;1
IMO B

Bunuel wrote:
The Number of students learning three subjects are as follows

Maths = 40
English = 50
Science = 35

If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?

A. 0
B. 1
C. 25
D. 35
E. 45


Are You Up For the Challenge: 700 Level Questions
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Re: If the Number of students learning exactly two subjects is maximum and  [#permalink]

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New post 31 Dec 2019, 11:49
nick1816 wrote:
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'
we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62


Sorry where did you get this? Is is another formula?

The formula I am aware of is Total = A+B+C-(sum of exactly 2 overlap) -2(sum of all 3 overlap)+Neither

or, Total = 40+50+35-(sum of exactly 2 overlap) -2(0)+0
or total = 125 - (sum of exactly 2 overlap)
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Re: If the Number of students learning exactly two subjects is maximum and  [#permalink]

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New post 31 Dec 2019, 17:10
1
N(maths)= a+b+d+e

N(English)= b+c+e+f

N(Science)= d+e+f+g

N(maths)+N(English)+N(Science)
= a+b+d+e+b+c+e+f+d+e+f+g
= a+c+g+2(b+d+f)+3e

Now we need to figure out students learning exactly one subject, that is a+c+g.

a+c+g= N(maths)+N(English)+N(Science)-2(b+d+f)-3e


It's always better to draw venn diagram and look for what you need to figure out. (Don't just cram the formulas)


AnirudhaS wrote:
nick1816 wrote:
Assume number of students learning exactly two subjects is 'x', and number of students learning exactly one subject is 'y'
we have to minimize, y=40+50+35-2*x=125-2x
minimum value of y is 1 {odd-even= odd}, when x=62


Sorry where did you get this? Is is another formula?

The formula I am aware of is Total = A+B+C-(sum of exactly 2 overlap) -2(sum of all 3 overlap)+Neither

or, Total = 40+50+35-(sum of exactly 2 overlap) -2(0)+0
or total = 125 - (sum of exactly 2 overlap)

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Re: If the Number of students learning exactly two subjects is maximum and   [#permalink] 31 Dec 2019, 17:10
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