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Of the 200 candidates who were interviewed for a position...

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Of the 200 candidates who were interviewed for a position...

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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
B. 10
C. 18
D. 20
E. 25

The OA is B.

Experts, any suggestion about how to solve this PS question? Thanks in advance.

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LUANDATO wrote:
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
B. 10
C. 18
D. 20
E. 25

The OA is B.

Experts, any suggestion about how to solve this PS question? Thanks in advance.
The total number of employees = 200 are distributed as following:

    Employees with 2-Wheeler = x = 100;
    Employees with Credit Card = y = 70;
    Employees with Mobile phone = z = 140;

    Employees with 2-Wheeler & Credit Card = (x & y) = 40;
    Employees with 2-Wheeler & Mobile phone = (x & z) = 60;
    Employees with Credit Card & Mobile phone = (y & z) = 30;

    Employees with all the three = (x & y & z) = 10

    Employees with none of the three = p

We have to get the value of p.

Thus,

200 = x + y + z - (x&y) - (y&z) - (x&z) + (x & y & z) + p

200 = 100 + 70 + 140 - 40 - 60 - 30 + 10 + p

p = 10

The correct answer: B

Hope this helps!
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Manhattan Review GMAT Prep

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LUANDATO wrote:
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
B. 10
C. 18
D. 20
E. 25
We can create the equation:

Total = two-wheeler + credit card + mobile phone - doubles + triple + neither

200 = 100 + 70 + 140 - (40 + 30 + 60) + 10 + n

200 = 310 - 130 + 10 + n

200 = 190 + n

10 = n

Answer: B

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Jeffrey Miller Head of GMAT Instruction

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