Rubella & Mumps

Answer [spoiler]{C}[/spoiler]

We need to find "NoT M" = 15000 - 5000 = 10000

I told you what the official answer is... it's not D.

fourteenstix wrote:I told you what the official answer is... it's not D.

Sorry, mistakenly missed the word "only" in the last line.. indeed its [spoiler]{C}[/spoiler] only

This is how I approached the problem:

1) Draw a Venn Diagram and let R be the number of children that have been vaccinated only against rubella; X be the number of children that have been vaccinated against both; and M be the number of children that have been vaccinated only against mumps.
2) Write out the given information in equations:
R + X = 2 (M + X)
X = 2M
X = 5,000
3) Begin solving:
5,000 = 2M; M = 2,500
R + 5,000 = 2 (2,500+5,000); R = 15,000 - 5,000; R = 10,000

No offense, but can someone other than theCodeToGMAT please answer?

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.

plug in easy numbers

let mumps = 6, rubella = 12
let both = 4, left for only mumps = 6 - 2 = 4, which doubles only mumps as given in condition
only rubella 12 - 4 = 8, twice of both
if both = 4 then only rubella = 8
if both = 5000 then only rubella = 10000