Inflammation/fever

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eustudent: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun May 31, 2009 10:17 pm; Thanked: 1 times

by eustudent » Tue Sep 01, 2009 2:21 pm

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.

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Source: Beat The GMAT — Data Sufficiency | Tue Sep 01, 2009 2:21 pm

Matmasi: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Jul 24, 2009 2:58 am; Thanked: 2 times

by Matmasi » Tue Sep 01, 2009 2:35 pm

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

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eustudent: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Sun May 31, 2009 10:17 pm; Thanked: 1 times

by eustudent » Tue Sep 01, 2009 4:58 pm

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!

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

by mehravikas » Tue Sep 01, 2009 6:11 pm

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

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Matmasi: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Jul 24, 2009 2:58 am; Thanked: 2 times

by Matmasi » Wed Sep 02, 2009 1:10 am

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).

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JeffB: Master | Next Rank: 500 Posts; Posts: 153; Joined: Tue Jun 02, 2009 2:48 pm; Location: Ohio; Thanked: 16 times

hmm

by JeffB » Wed Sep 02, 2009 6:31 am

Overlapping Sets Charts.

Attachments

Book1.xlsx: (10.74 KiB) Downloaded 168 times

Last edited by JeffB on Wed Sep 02, 2009 6:42 am, edited 1 time in total.

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iamaneophyte: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Wed Aug 19, 2009 11:29 am

Answer is C

by iamaneophyte » Wed Sep 02, 2009 6:32 am

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!

neophyte

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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 amFollowed by: 1 member; Location: Sydney; Thanked: 23 times

Re: hmm

by mehravikas » Wed Sep 02, 2009 12:13 pm

thanks...

JeffB wrote:Overlapping Sets Charts.

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