Last visit was: 12 Aug 2024, 22:46 It is currently 12 Aug 2024, 22:46
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Request Expert Reply

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

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 11 Aug 2007
Posts: 20
Own Kudos [?]: 117 [107]
Given Kudos: 0
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649119 [35]
Given Kudos: 86922
General Discussion
Intern
Joined: 11 Aug 2007
Posts: 20
Own Kudos [?]: 117 [2]
Given Kudos: 0
Intern
Joined: 24 Jul 2007
Posts: 23
Own Kudos [?]: 18 [2]
Given Kudos: 0
Re: GMAT prep 1, Q26 (DS) [#permalink]
1
Kudos
1
Bookmarks
elgo wrote:
Obviously, smth is wrong with my brain, but I couldn't understand the OA...

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

any thoughts?

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

1000-880(neither)-20(fever) =100
SVP
Joined: 07 Jul 2004
Posts: 2001
Own Kudos [?]: 1926 [3]
Given Kudos: 0
Location: Singapore
[#permalink]
2
Kudos
1
Bookmarks
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.
Intern
Joined: 07 May 2014
Posts: 19
Own Kudos [?]: 30 [4]
Given Kudos: 26
Concentration: International Business, Technology
Re: When 1,000 children were inoculated with a certain vaccine [#permalink]
4
Kudos
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?
Intern
Joined: 17 Jan 2014
Posts: 11
Own Kudos [?]: 8 [5]
Given Kudos: 14
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
4
Kudos
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.
Attachments

Untitled.jpg [ 21.1 KiB | Viewed 62477 times ]

Manager
Joined: 15 Nov 2006
Affiliations: SPG
Posts: 232
Own Kudos [?]: 3222 [0]
Given Kudos: 34
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Top Contributor
Bunuel wrote:
dhirajx wrote:
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?

No, you cannot assume that. It's vise-versa, if there is no overlap, then you'd be told that in one way or another.

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

Attachment:
Untitled.png

Answer: C.

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

Hope this helps.

Bunnel - do you have a rule of thumb about when to use Venn Diagram and when to use matrix table?
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649119 [1]
Given Kudos: 86922
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
1
Kudos
Expert Reply
dimitri92 wrote:
Bunuel wrote:
dhirajx wrote:
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?

No, you cannot assume that. It's vise-versa, if there is no overlap, then you'd be told that in one way or another.

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

Attachment:
Untitled.png

Answer: C.

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

Hope this helps.

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.
Manager
Joined: 15 Nov 2006
Affiliations: SPG
Posts: 232
Own Kudos [?]: 3222 [0]
Given Kudos: 34
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Top Contributor
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?
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649119 [0]
Given Kudos: 86922
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Expert Reply
dimitri92 wrote:
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:
Director
Joined: 12 Nov 2016
Posts: 569
Own Kudos [?]: 119 [1]
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
[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
Senior Manager
Joined: 05 Jan 2017
Posts: 412
Own Kudos [?]: 288 [0]
Given Kudos: 15
Location: India
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
elgo wrote:
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

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
Intern
Joined: 06 Oct 2017
Posts: 8
Own Kudos [?]: 10 [0]
Given Kudos: 6
When 1,000 children were inoculated with a certain vaccine, [#permalink]
Bunuel wrote:
dhirajx wrote:
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?

No, you cannot assume that. It's vise-versa, if there is no overlap, then you'd be told that in one way or another.

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

Answer: C.

Theory on Overlapping Sets:
https://gmatclub.com/forum/advanced-over ... 44260.html
https://gmatclub.com/forum/how-to-draw-a ... 98036.html

All DS Overlapping Sets Problems to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=45
All PS Overlapping Sets Problems to practice: https://gmatclub.com/forum/search.php?se ... &tag_id=65

Hope this helps.

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..
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649119 [0]
Given Kudos: 86922
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Expert Reply
Pratyaksh2791 wrote:
Bunuel wrote:
dhirajx wrote:
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?

No, you cannot assume that. It's vise-versa, if there is no overlap, then you'd be told that in one way or another.

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

Answer: C.

Hope this helps.

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.
Intern
Joined: 13 Sep 2013
Posts: 6
Own Kudos [?]: 4 [1]
Given Kudos: 14
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
1
Kudos
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.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30998 [0]
Given Kudos: 799
Location: Canada
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Expert Reply
Top Contributor
elgo wrote:
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

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:
VP
Joined: 18 Dec 2017
Posts: 1161
Own Kudos [?]: 1062 [0]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
elgo wrote:
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

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.
Intern
Joined: 02 Feb 2022
Posts: 15
Own Kudos [?]: 3 [1]
Given Kudos: 17
Location: Hong Kong
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
1
Kudos
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
Non-Human User
Joined: 09 Sep 2013
Posts: 34396
Own Kudos [?]: 862 [0]
Given Kudos: 0
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: When 1,000 children were inoculated with a certain vaccine, [#permalink]
Moderator:
Math Expert
94906 posts