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

Question

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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ScottTargetTestPrep · Accepted Answer

Solution:
 
Let ME, MS, and ES be the number of students who study Math and English, Math and Science, and English and Science, respectively. So we have 40 - (ME + MS), 50 - (ME + ES), and 35 - (MS + ES) as the number of students who study only Math, only English, and only Science, respectively. Therefore, the total number of students who study only one subject is:

40 - (ME + MS) + 50 - (ME + ES) + 35 - (MS + ES)

125 - 2(ME + MS + ES)

Since we want to minimize this value and we see that if ME + MS + ES = 62, the value of 125 - 2(ME + MS + ES) will be minimized, and that value is 125 - 2(62) = 1.

Answer: B

nick1816 · Answer

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

Archit3110 · Answer

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

AnirudhaS · Answer

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)

nick1816 · Answer

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)

bhupendersingh27 · Answer

Maths = 40
English = 50
Science = 35

Total number of students = 125
maximum how many students can be assigned two subjects: 2 x (125/2) = 2 X(62.5) ~ 2 x (62) = 124.
so 1 student left when number of students learning exactly two subjects is maximum.

naveenban2 · Answer

bhupendersingh27  Total number of students is not 125. Number of students in individual subjects contain the number the number of students common to other subjects.
Can you please explain the Formula used by you ? 2 x (125/2) = 2 X(62.5) ~ 2 x (62) = 124.

adewale223 · Answer

Very simple way to solve the problem

Let a be sum of only one

b sum of only two

c sum of only three

a + 2b + 3c = 125

Since c = 0

a + 2b = 125

Since 2b is even, maximum number for 2b will be 124

So a is 1

Answer choice B

axeofflane · Answer

Beautiful question tbh

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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