When 1,000 children were inoculated with a certain vaccine, some developed inflammation at the site of the inoculation

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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


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BTGmoderatorDC wrote:
Wed Nov 02, 2022 4:49 am
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


OA 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:
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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.youtube.com/watch?v=jK-tiBrrf04
Brent Hanneson - Creator of GMATPrepNow.com
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