Data Sufficiency

Hi,
This problem has been posted before, however, I cannot quite get the explanations given. Can someone attempt to explain to me a bit more clearly than the previos posts?!

When 1,000 children were inoculated with a certain vaccine, some developed inflammation at the site of the inoculation and some developed fever. How many of the children developed inflammation but not fever ?

(1) 880 children developed neither inflammation nor fever
(2) 20 children developed fever
So, We have Inflamation (I)
Fever (F)
I+F+Neither- Both= Grand total.
We have
880(neither)+20(fever)+ I(unknown)- Both(unknown)=1000
I=?
Answer is C.I must have missed something because I cannot find the value of the children that have Both.
Please help.

Hi,

how you wrote we need to apply this formula:
I+ F + Neither - Both = Grand total
But first, let's clarify what we are looking for.
We are asked to find the number of child who developed inflammation but not fever.
This is equal to the number of children who got an inflammation minus the number of children who got inflammation + fever.
In other words, if you have 4 guys with inflammation and 2 of them have also fever, the number of guys with just inflammation is 4-2=2.

So:

Inflammation - I
Fever - F

Total = F + I - Both (I+F) + Neither (I+F)

Statements 1 & 2 are clearly insufficient alone.

Combining 1 & 2

1000 = 20 + (I - Both (I+F)) + 880

I - Both (I+F) = 100

Sufficient.

Best regards

I understand what you mean, but I still do not feel confident that we have the number of people who have both.

I am aware of this formula, but this is where I lose the line of reasoning.
GT= Group 1+ Group 2+ Neither Group- Both groups.
GT= 1000
NG= 880
G1(F)= 20
G2(I)= ?
BG=?
So, I have two unknowns, 1st is the Inflamation and 2nd is Both Groups?
or 1000- 880=120; 120 is both groups?
Because I cannot have two unknown, I put E as an answer. I mean considering both, I still can't get to the solution.
Please help, because I always score badly on this type DS qusetions!

answer should be 'E'. We have two unknowns and it is not possible to calculate the value of people having inflammation but not fever.

OK, try to imagine:
There is a group of 10 people.
4 are not sick, so don't have fever or iflammation.
4 have inflammation
4 have fever.
You see the the sum is 12? but we have 10 people..
This happens because someone of them has inflammation and has also fever.

in fact 2 have both inflammation and fever.
So, the number of people who ONLY got inflammation and NOT fever is equal to the number of people who got inflammation less the number of people that got both.

And to answer to mehravikas, your reasoning is wrong because the question is NOT asking the value of I, but the value of I-(BothI&F).

Overlapping Sets Charts.

Out of 1000 people, 880 didn't get affected either with inflammation or fever. So the remaining children are 120.

These are the children who are affected with inflammation or fever or both.

With fever alone is 20 and so remaining would be 100.

Hope this helps!

thanks...

JeffB wrote:Overlapping Sets Charts.