Question: 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?

1. 0
2. 10
3. 18
4. 20
5. 25

Answer: B

Solution and Explanation:

Approach Solution 1:

Given that there were 200 call centre employees, 100 of them had two-wheelers, 70 had credit cards, 140 had mobile phones, 40 of them owned both a two-wheeler and a credit card, 30 owned both a credit card and a mobile phone, 60 owned both a two-wheeler and a mobile phone, and 10 owned all three.

The following equation can be made:

Total equals two-wheeler plus credit card plus mobile phone minus doubles, triples, and neither

200 = 100 + 70 + 140 - (40 + 30 + 60) + 10 + n
200 = 310 - 130 + 10 + n
200 = 190 + n
10 = n
Response: B

Approach Solution 2:

Given that there were 200 call centre employees, 100 of them had two-wheelers, 70 had credit cards, 140 had mobile phones, 40 of them owned both a two-wheeler and a credit card, 30 owned both a credit card and a mobile phone, 60 owned both a two-wheeler and a mobile phone, and 10 owned all three.
Total candidates = 200.

So, 100 = A, 70 = B, and 140 = C, giving a total of 200.
40 = A n B (Indicating intersection with n) (Indicating intersection with n)
30 = B n C
60 = A n C
10 = A n B n C
Utilizing the formula AUBUC = A + B + C - A n B + B n C + C n A + A n B n C

you’ll get 200 = 190. So there are 10 people missing . So 10 is the correct choice.
B is the right choice.

“Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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