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Vaccinated Against Rubella

This topic has 3 expert replies and 1 member reply
bml1105 Master | Next Rank: 500 Posts
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Vaccinated Against Rubella

Post Tue Jun 03, 2014 2:29 pm
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 5,000 have been vaccinated against both, how many have been vaccinated only against rubella?

(A) 2,500
(B) 7,500
(C) 10,000
(D) 15,000
(E) 17,500


OA: C

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Post Wed Nov 08, 2017 4:25 pm
bml1105 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 5,000 have been vaccinated against both, how many have been vaccinated only against rubella?

(A) 2,500
(B) 7,500
(C) 10,000
(D) 15,000
(E) 17,500
We can create the following formula:

Total = total mumps + total rubella - both + neither

We can let total mumps = m, and thus total rubella = 2m.

We can let both = b, and thus only mumps is m - b.

Since the number who have been vaccinated against both is twice the number who have been vaccinated only against mumps:

b = 2(m - b)

b = 2m - 2b

3b = 2m

Since b = 5000, we have:

3(5000) = 2m

15000 = 2m

7500 = m

Since m = 7500, the total number of children vaccinated against rubella is r = 2m = 2(7500) = 15000. Thus, the number who have been vaccinated against only rubella is r - b = 15000 - 5000 = 10000.

Answer: C

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Jeffrey Miller Head of GMAT Instruction

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GMAT/MBA Expert

Post Wed Jun 04, 2014 7:13 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

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 our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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

Easy Problem Solving questions
- http://www.beatthegmat.com/the-aam-aadmi-party-t272242.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

Medium Problem Solving questions
- http://www.beatthegmat.com/probability-question-t273360.html
- http://www.beatthegmat.com/posted-speed-limit-t272374.html
- http://www.beatthegmat.com/motel-t271938.html
- http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
- http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html

Difficult Problem Solving questions
- http://www.beatthegmat.com/ratio-problem-t268339.html
- http://www.beatthegmat.com/overlapping-sets-question-t265223.html
- http://www.beatthegmat.com/fractions-t264254.html
- http://www.beatthegmat.com/overlapping-sets-t264092.html
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
- http://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- http://www.beatthegmat.com/sets-matrix-ds-t271914.html
- http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
- http://www.beatthegmat.com/a-manufacturer-t270331.html
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- http://www.beatthegmat.com/double-set-matrix-question-t271423.html
- http://www.beatthegmat.com/sets-t269449.html
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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GMAT/MBA Expert

Post Tue Jun 03, 2014 6:54 pm
Quote:
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:


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


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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Mitch Hunt
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GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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GyanOne Master | Next Rank: 500 Posts
Joined
01 Dec 2011
Posted:
225 messages
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9 members
Upvotes:
16
Post Wed Jun 04, 2014 6:23 am
From the question statement, we can surmise:

Number vaccinated against both = 5000
Number vaccinated only against Mumps = 2500

Number vaccinated against mumps = Number vaccinated only against mumps + Number vaccinated against both = 5000 + 2500 = 7500

Number vaccinated against Rubella = 2 * 7500 = 15000

Number vaccinated against only Rubella = Number vaccinated against Rubella - Number vaccinated against both = 15000 - 5000 = 10,000

Option (C).

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