When 1,000 children were inoculated with a certain vaccine, some developed inflammation

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri Aug 14, 2020 1:10 pm

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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
Source: GMAT prep

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 14, 2020 1:10 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: When 1,000 children were inoculated with a certain vaccine, some developed inflammation

by Brent@GMATPrepNow » Sat Aug 15, 2020 8:06 am

BTGModeratorVI wrote: ↑
Fri Aug 14, 2020 1:10 pm
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
Source: GMAT prep

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:

Brent Hanneson - Creator of GMATPrepNow.com

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: When 1,000 children were inoculated with a certain vaccine, some developed inflammation

by deloitte247 » Sat Aug 15, 2020 12:14 pm

Total children = 1000
Let children with fever only = f
Let children with inflammation only = i
Let children with neither fever nor inflammation = n
Let children with both fever and inflammation = b

Target question => How many of the children developed inflammation but no fever?
Find i

Total = f + i + n + b and total (f) = f + b

Statement 1 => 880 children developed neither inflammation nor fever
i.e n = 880
= 880 + f + i + b
There are 3 unknown variables and target question cannot be answered. Statement 1 is NOT SUFFICIENT

Statement 2 => 20 children developed fever
i.e total (f) = f + b and total (f) = 20
Therefore, 1000 = n + i + 20
There are 2 unknown variables and target question cannot be answered. Statement 2 is NOT SUFFICIENT

Combining both statements together =>
From statement 1 => n = 880
From statement 2 => f + b = 20
From question stem => total children = 1000
Total children = f + i + n + b
1000 = 880 + 20 + i
1000 = 900 + i
i = 1000 - 900
i = 100

100 children developed inflammation but no fever. Both statements combined together ARE SUFFICIENT

Answer = C

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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: When 1,000 children were inoculated with a certain vaccine, some developed inflammation

by swerve » Sat Aug 15, 2020 12:23 pm

BTGModeratorVI wrote: ↑
Fri Aug 14, 2020 1:10 pm
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
Source: GMAT prep

Total $=$ children(nothing) $+$ children(fever only) $+$ children (inflammation only) $+$ children (both) children(fever) $=$ children(fever only) $+$children(both)

Statement 1: $1000 = 880 +$ children(fever only) $+$children (inflammation only) $+$children (both). Three variables, one equation. INSUFFICIENT $\Large{\color{red}\chi}$
$1000 = 880 +$Children (fever) $+$ Children (inflammation only)

Statement 2: $20 =$ children(fever only) $+$children(both)
therefore $1000 =$ children(nothing) $+$ 20 $+$children (inflammation only)
INSUFFICIENT $\Large{\color{red}\chi}$

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

children (Inflammation only) $= 100$. $\Large{\color{green}\checkmark}$

Therefore, C

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