Problem Solving

Question 2
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. 20
C. 10
D. 18
E. 25
[spoiler]
The correct choice is (C) and the correct answer is 10.

Explanatory Answer
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.
[/spoiler]

https://www.beatthegmat.com/very-interst ... t9806.html

This thread doesn't talk about this particular question. However, it does talk about the formula. I found this thread to very helpful.

i'm confused.

two wheeler plus mobile = 60
two wheeler plus credit card = 40
all three = 10

60 + 40 + 10 > 100

how can these three numbers combined be greater than the total number of two wheelers?

mandryd wrote:i'm confused.

two wheeler plus mobile = 60
two wheeler plus credit card = 40
all three = 10

60 + 40 + 10 > 100

how can these three numbers combined be greater than the total number of two wheelers?

Because you can't add 60+40+10. The 10 has already been counted twice since they that two wheeler plus mobile and they have the two wheeler plus credit card.

That is just like asking how there can be 100 that have two wheelers and 70 that have mobile and 140 that have credit cards and this = 310, which is > 200 candidates.

-Carrie

I'm no expert, so I am wondering why the follow didn't work:

200=a+b+c-ab-bc-ac-2(abc)+neither

Plugging in the numbers, I got:

200=360+N

N = 160

What steps am I missing?

gaggleofgirls wrote:

mandryd wrote:i'm confused.

two wheeler plus mobile = 60
two wheeler plus credit card = 40
all three = 10

60 + 40 + 10 > 100

how can these three numbers combined be greater than the total number of two wheelers?

Because you can't add 60+40+10. The 10 has already been counted twice since they that two wheeler plus mobile and they have the two wheeler plus credit card.

That is just like asking how there can be 100 that have two wheelers and 70 that have mobile and 140 that have credit cards and this = 310, which is > 200 candidates.

-Carrie

Ah okay thanks. Dunno why I got confused on that. The poor comma usage in the question probably set me off. haha.

ellexay wrote:I'm no expert, so I am wondering why the follow didn't work:

200=a+b+c-ab-bc-ac-2(abc)+neither

Plugging in the numbers, I got:

200=360+N

N = 160

What steps am I missing?

This formula won't work here.


= a+b+c - (candiates exactly has only 2 things) - 2*(exactly has 3 things)



candidates with two wheelers and credit card (T C) = 40
candidates have only two wheelers and credit card (no Mobile Phones) = 40-10 =30

similarly C M - > 30-10=20
similary T M -60 -->60-10 =50

Now you can apply your formula
= 70+100+140 - (30+20+50) -2(10)
= 310 - 120 = 190

Final Anser = 200-190 =10