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Rubella

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by lukaswelker » Thu Apr 17, 2014 8:31 am
Hey Guys

I'm lacking the obvious math equation here,

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?

2500 : 7500 : 10000 : 15000 : 17500

Please help me :)
Cheers
Lukas
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by GMATGuruNY » Thu Apr 17, 2014 10:13 am
lukaswelker wrote: In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?

2500 : 7500 : 10000 : 15000 : 17500
This is an EITHER/OR group problem.
Every child EITHER has been vaccinated against mumps OR has not.
Every child EITHER has been vaccinated against rubella OR has not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

Let M = mumps, NM = not mumps, R = rubella, NR = not rubella.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.

The number who have been vaccinated against both is twice the number of who have been vaccinated against only mumps:
Image

The number who have been vaccinated against rubella is twice the number who have been vaccinated against mumps:
Image

5000 have been vaccinated against both:
According to the grid, both = 2x = 5000 and only rubella = 4x = 10,000.

The correct answer is C.
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by Brent@GMATPrepNow » Thu Apr 17, 2014 10:20 am
I thought I'd point out that Mitch's "group grid" (aka Double Matrix Method) can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of children, and the two characteristics are:
- vaccinated against mumps or not vaccinated against mumps
- vaccinated against rubella or not vaccinated against rubella

To learn more about the Double Matrix Method, watch our free 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/the-aam-aadm ... 72242.html
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Difficult Problem Solving questions
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- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- 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://www.beatthegmat.com/double-set-m ... 71423.html
- 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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