One hundred management students who read at least one of the three bus

Question

One hundred management students who read at least one of the three business magazines are surveyed to study the readership pattern. It is found that 80 read Business India, 50 read Business world, and 30 read Business Today. Five students read all the three magazines. How many read exactly two magazines?

(A) 50
(B) 55
(C) 65
(D) 95
(E) 100

(A) 50 
(B) 55
(C) 65 
(D) 95
(E) 100

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Kinshook · Answer

Given: One hundred management students who read at least one of the three business magazines are surveyed to study the readership pattern. It is found that 80 read Business India, 50 read Business world, and 30 read Business Today. Five students read all the three magazines. 
Asked: How many read exactly two magazines?

Total = 1 + 2 + 3 - Exactly 2 - 2* Exactly 3 + None
100 = 80 + 50 + 30 - Exactly 2 - 2*5 + 0
100 = 150 - Exactly 2
Exactly 2 = 50

IMO A

anjanita · Answer

The answer is A

Let us assume the number of students read Business India & read Business world = x
No. of Students read Business world & Business Today = y
No. of Students read Business India & Business Today = z

Therefore, 100=80+50+30−(x+5)−(y+5)−(z+5)+5

x+y+z=80+50+30+5−15−100

x+y+z=50

The number of students who read exactly two magazines =50

ScottTargetTestPrep · Answer

Solution:

We can use the formula:

Total = India + World + Today - (Exactly Two) - 2 * (All Three) + None

100 = 80 + 50 + 30 - x - 2(5) + 0

100 = 150 - x

x = 50

Answer: A

Fdambro294 · Answer

Let:

X = people who read only 1 mag

Y = people who read exactly 2 mags

Z = people who read exactly 3 mags = 5

Question asks for: what is Y = ?

100 people = X + Y + Z

Z = 5, so:

95 = X + Y (eq 1)

All together, there are 160 “hits” in total of what ppl say they read.

The people who only read 1 magazine will be responsible for just 1 of these recorded readings.

Each person who reads exactly 2 magazines will be responsible for 2 of these recorded readings

And each person who reads exactly 3 magazines will be responsible for 3 of these recorded readings.

160 = X + 2Y + 3Z

since Z = 5 and 3Z = 15

145 = X + 2Y (eq 2)

Take (eq 2) and subtract (eq 1):

145 = X + 2Y
(-) (95 = X + Y)
_____________

50 = Y = no of ppl who read exactly 2 mags

A

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One hundred management students who read at least one of the three bus

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One hundred management students who read at least one of the three bus

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