Jill has applied for a job with each of two different companies. What

Hi dave13,

Well if you are aware of the two set theory, it would be simple to visualize Set A as Company M and Set B as comapnay N

So in two set theory we have
Only A=a, Only B=b, Both A&B=x, neither=n and total=T.
Where Total= only A + Only B +A&B+ n
T=a+x+b+n

Set A= only A and A&B = a+x
Set B= only B and A&B= b+x
Both A&bB=x
or
you also want to remember the other form.
Total= Set A +Set B -Both A&B +neither
T= (a+x)+(b+x)-x+n
which is precisely
T=a+x+b+n.

Now coming back to this question
We know that total =1 . Why you may ask. Probability of any event occurring lies between o and 1
We generally say Probability of an event happening + probability of event not happening =1
We are supposed to find the value of x. What will help us reach that.

T-a-b-n=x
1-a-b-n=x
or
Set A+Set B+n -Total= Both

Either we are given Set A, & Set B and Neither.
or
We are given the values of only A Only B and neither.

So statements 1: We are given the value of n and but in absence of any other information this no way leads us to our goal.So INSUFFICIENT

So statements 2: This gives us a lot of information about only A=a and only B=b . Great but we do need the value of neither to calculate both. So INSUFFICIENT

Why does this statement give information about only A , Only B. In mathematics OR represents addition , AND represents multiplication. We are told that she gets job offer from exactly one. What are the elements that represent exactly one only a , only b. This means she gets job offer from only a OR she gets jobs offer from only B

then only a or only b=0.5
this means that only a+only b =0.5

Now since we know what all information is given in two statements, surely should we combine them we get the values of only A=a,only B=b, neither =n
from this
1-a-b-n=x
1-(0.5)-(0.3)=x
or x= 0.2
Hence both statements are required to find the value of "BOTH" which is asked in question So C is sufficient to answer the question

Probus