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
Vaccinated Against Rubella
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- GMATGuruNY
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This is an EITHER/OR group problem.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
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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- GyanOne
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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).
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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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: 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
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html
Difficult Problem Solving questions
- 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.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
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: 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
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html
Difficult Problem Solving questions
- 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.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
GMAT/MBA Expert
- Jeff@TargetTestPrep
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We can create the following formula: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
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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- fskilnik@GMATH
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Excellent opportunity to blend two techniques: Venn diagrams ("overlapping sets") and the k technique !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
(Hint: understand the values presented in increasing order of letter sizes!)
$$? = 4k$$
$$2k = 5,000\,\,\,\, \Rightarrow \,\,\,\,? = 10,000$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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