Vaccinated Against Rubella

[bml1105]

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

[GMATGuruNY]

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.

[GyanOne]

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).

[Brent@GMATPrepNow]

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
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Medium Problem Solving questions
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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

[Jeff@TargetTestPrep]

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

[fskilnik@GMATH]

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

Excellent opportunity to blend two techniques: Venn diagrams ("overlapping sets") and the k technique !

(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.