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After qualifying out of 400 professionals, 112 joined industry, 120 started practice and 160 joined as paid assistants. There were 32, who were in both practice and service 40 in both practice and assistantship and 20 in both industry and assistantship. There were 12 who did all the three. Find how many of them did only one of these.
  • a)
    88
  • b)
    244
  • c)
    122
  • d)
    None
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
After qualifying out of 400 professionals, 112 joined industry, 120 st...
Total =  400
Industries Service  S  = 112
Practice  P = 120
Paid Assistant A = 160
P ∩ S = 32
P ∩ A = 40
S ∩ A = 20
P ∩ S ∩ A  = 12
Total = S + P + A - P ∩ S - P ∩ A - S ∩ A + P ∩ S ∩ A + None
400 = 112 + 120 + 160 - 32 - 40 - 20 + 12 + None
None = 88
Person = 400 - 88 = 312
312 - (32 - 12) - (40-12) -(20-12) - 12
= 312 - 20 - 28 - 8 - 12
= 244
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Most Upvoted Answer
After qualifying out of 400 professionals, 112 joined industry, 120 st...
Given Information:
Out of 400 professionals,
112 joined industry,
120 started practice,
160 joined as paid assistants.

There were 32, who were in both practice and service,
40 in both practice and assistantship and
20 in both industry and assistantship.
There were 12 who did all the three.

To Find: How many of them did only one of these.

Solution:
Let's assume the number of professionals who only joined the industry, practice, and assistantship be I, P, and A respectively.

Total number of professionals = 400

From the given data, we can form the following equations:

I + P + A = 400 --- Equation (1)

I + 20 + 40 - 12 = 112 => I = 54 --- Equation (2)

P + 20 + 32 - 12 = 120 => P = 80 --- Equation (3)

A + 40 + 32 - 12 = 160 => A = 100 --- Equation (4)

Therefore, the number of professionals who did only one of these is:

I + P + A - (20 + 32 + 40) + 12 = 54 + 80 + 100 - 92 = 142 - 92 = 50

Hence, the correct option is (a) 88.
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After qualifying out of 400 professionals, 112 joined industry, 120 st...
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