When 1,000 children were inoculated with a certain vaccine,

The answer is C, combine the 2 statements and its sufficient

1000-880(neither)-20(fever) =100

St1:
just tells us that #(inflmmation only) + #(fever only) + #(both fever and inflmmation) = 120. Insufficient.

St2:
Just tells us if #(fever and inflmmation) = x, then #(fever only) = 20-x. Insufficient.

St1 and St2:
#(inflmmation only) = I-x
#(inflmmation and fever) = x
#(fever only) = 20-x

So I-x + x + 20-x = 120
I-x = 100
#(inflmmation only) = 100

Sufficient.

Ans C

P.S: Solved using Venn Diagram.

It seems there is no detail about children developing inflammation and fever. It is safe to assume there is no A∩B unless it is clearly mentioned in the question?

Hello,

I tried solving this question through Venn Diagram. Putting the attachment here. Could anyone please let me know where am I lacking?
Total Sample = 1000
Neither I nor Fever = 880
Remaining = 120 with either Fever or Inf. or both.
Fever = 20

So, only Inflammation or Inflammation and fever = 100

And hence, according to me, I can't find the answer for the question, hence Statements are insufficient.

Bunnel - do you have a rule of thumb about when to use Venn Diagram and when to use matrix table?

For 2 groups I almost always use a matrix.

Thanks for the quick response Bunnel.
May be I am doing something wrong here and not seeing the right logic. I will appreciate your help here:
I don't see two groups. I see one group of kids who can either get one ailment or another. How do we decide if the groups are two or one?

Please check the matrix below:

[quote="elgo"]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[/quote

In order to solve this question we need to know the number of children who developed neither and the number of children who developed fever- it is important to note this is a binary group- based on the stimulus it is assumed that there is no group that developed inflammation and fever at the site of inoculation.

Statement (1) gives us only one piece of the equation. Insufficient

Statement (2) still leaves us with the variable of the number of children who developed neither inflammation nor fever. Insufficient.

Statement (1) and Statement (2) together allow us the calculate the number of children who developed inflammation- only because there is no overlap with these groups

Total= A + B - Neither ( in this scenario A cannot be A + C (overlap) because it is inferred from the problem, again, you either have developed inflammation or have developed a fever)
1000= A + 20- 880
120= A + 20
100= A

total = children(nothing) + children(fever only) +children (inflammation only) +children (both)
children(fever) = children(fever only) +children(both)

St1: 1000 = 880 + children(fever only) +children (inflammation only) +children (both). three variables. one equation.INSUFFICIENT
1000 = 880 +Children (fever) + Children (inflammation only)

St 2: 20 = children(fever only) +children(both)
therefore 1000 = children(nothing) + 20 +children (inflammation only)

St 1 & St 2: 1000 = 880 +20 +Children(inflammation only)

children (Inflammation only) = 100. ANSWER

Option C

Hi Bunuel,

I have a question here.. Usually the formula for two groups is :

Total = Group A+ Group B+ Neither - Both

In this question, why are we missing out the case for Both?

On combining both the statements:

1000= 20(Fever)+X (for Inflammation) +880 (Neither) - Both(Suffering from both)

So we have two unknown variables X and Both..

Answer should E in that case..

If you re-read the solution you quote carefully, you'll see that we can solve this particular question without that formula and without knowing both.

If I understand correctly here we are assuming that when they say 20 children developed fever it included both children who only developed fever and children who developed both fever and inflammation? Because generally questions like this would mention children having fever separately and children having both fever and inflammation separately - making this question vague. It should clearly mention in the question what there statements imply.

Target question: How many of the children developed inflammation but not fever?

One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of 1000 children, and the two characteristics are:
- inflammation or no inflammation
- fever or no fever

So, we can set up our matrix as follows:

Noticed that I placed a red star in the box representing our target question (the number of children who developed inflammation but not fever)

Statement 1: 880 children developed neither inflammation nor fever.
We can place that information here:


We still don't have enough information to determine the value that goes in the starred box
So, statement 1 is NOT SUFFICIENT

Statement 2: 20 children developed fever.
If 20 of the 1000 children developed a fever, then the remaining 980 children did NOT develop a fever.
We can place that information here:


We still don't have enough information to determine the value that goes in the starred box
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we COMBINE the statements we get:

This allows us to determine the value that goes in the starred box
So, the answer to the target question is 100 children developed inflammation but not fever

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:

Bunuel,

Just to make sure I am thinking straight on this one (Because I got it incorrect in my yesterday's attempt).

If the question was " The number of children who developed only fever" OR "The number of children who developed both" then the answer would have been E.

I know it's a fairly easy questions but it looks like that's what GMAT is best at : Make the easy questions tricky.

Considering the formula Total = A(Inflammation)+ B(Fever) - Both + Neither,
we can interpret that the question is asking for Inflammation - Both.

With (1) & (2) =>
1000 = Inflammation + 20 - Both + 880
Inflammation - Both = 100

Ans: C

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