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

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

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: — Data Sufficiency |

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

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

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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:
Image
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:
Image

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:
Image

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:
Image
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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: When 1,000 children were inoculated with a certain vaccine, some developed inflammation

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

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

by swerve » Sat Aug 15, 2020 12:23 pm

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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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