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23 Jan 2022, 02:44
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Of the 400 candidates who were interviewed for a position at a shopping mall, 200 had a two-wheeler, 140 had a credit card and 280 had a mobile phone. 80 of them had both, a two-wheeler and a credit card, 60 had both, a credit card and a mobile phone and 120 had both, a two wheeler and mobile phone and 20 had all three. How many candidates had none of the three?
A. 20
B. 40
C. 25
D. 15
E. 35
A. 20
B. 40
C. 25
D. 15
E. 35
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23 Jan 2022, 02:46
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Objective: Compute number of candidates who had none of the three.
Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three.
Total number of candidates = 400.
Number of candidates who had at least one of the three = n(A ∪ B ∪ C),
where A is the set of those who have a two wheeler, B is the set of those who have a credit card, and C is the set of those who have a mobile phone.
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - {n(A ∩ B) + n(B ∩ C) + n(C ∩ A)} + n(A ∩ B ∩ C)
Therefore, n(A ∪ B ∪ C) = 200 + 140 + 280 - {80 + 60 + 120} + 20
Or n(A ∪ B ∪ C) = 380.
n(A ∪ B ∪ C) is the number of candidates who had at least one of three.
As 190 candidates who attended the interview had at least one of the three,
(400 - 380 = 20) candidates had none of three.
Choice A is the correct answer.
Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three.
Total number of candidates = 400.
Number of candidates who had at least one of the three = n(A ∪ B ∪ C),
where A is the set of those who have a two wheeler, B is the set of those who have a credit card, and C is the set of those who have a mobile phone.
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - {n(A ∩ B) + n(B ∩ C) + n(C ∩ A)} + n(A ∩ B ∩ C)
Therefore, n(A ∪ B ∪ C) = 200 + 140 + 280 - {80 + 60 + 120} + 20
Or n(A ∪ B ∪ C) = 380.
n(A ∪ B ∪ C) is the number of candidates who had at least one of three.
As 190 candidates who attended the interview had at least one of the three,
(400 - 380 = 20) candidates had none of three.
Choice A is the correct answer.
23 Jan 2022, 02:49
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sajjad1995
Discussed here: of-the-200-candidates-who-were-interviewed-for-a-position-at-a-call-215086.html?fl=similar
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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