Question 12. Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

(a) 0

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(b) 20

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(d) 18

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Solution

The correct option is C (c) 10
(c)

Explanation: Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.

Total number of candidates = 200.

Number of candidates who had at least one of the three = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.

We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C

Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10

Or AUBUC = 190.
As 190 candidates who attended the interview had at least one of the three gadgets, 200 - 190 = 10 candidates had none of three.

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Similar questions

Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both two-wheeler and credit card, 30 had both credit card and mobile phone and 60 had both two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

Q. Of the 150 candidates who were interviewed for a position at a call center, 70 had a vehicle, 50 had their own home and 60 had a mobile phone. 20 of them had both a vehicle and a home, 15 had both a home and a mobile phone and 30 had both a vehicle and mobile phone, while 10 had all the three. How many candidates had none of the three?

उन 150 उम्मीदवारों में से जिनका कॉल सेंटर में एक पद के लिए साक्षात्कार किया गया था, 70 के पास एक वाहन था, 50 के पास अपना घर था और 60 के पास एक मोबाइल फ़ोन था। उनमें से 20 के पास वाहन और घर दोनों था, 15 के पास घर और मोबाइल फ़ोन दोनों था और 30 के पास वाहन और मोबाइल फ़ोन दोनों था, जबकि 10 के पास ये तीनों थे। कितने उम्मीदवारों के पास तीनों में से कुछ नहीं थे?

Q. One Hundred Twenty-five