Use a single variable as far as possible.

Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 5000 (so x = 2500)

Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*2500 = 10,000

Answer (C)
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C. 10,000

Let
R = vaccinated against Rubella
M = vaccinated against Measles
R'= not vaccinated against Rubella
M'= not vacinnated against Measles

Given RM = 5000, and R'M = 1/2 RM = 2500
M = 7500

R = 2 x M = 15000

RM' = R - RM = 15000 - 5000 = 10, 000

Answer: C

C

Make Venn Diagram.

Mumps = x
Rubella = 2x
Both = y

Only Mumps = x-y
As given y = 2(x-y)
i.e 3y = 2x
y = 5000
therefore x = 7500

Only Rubella = 2x-y = 2*7500 - 5000 = 10000
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A = Only Rubella
B = Both
C = Only Mumps

A + B = Total Rubella
B + C = Total Mumps

According to the question,

A + B = 2 ( B+ C ) --------------------- (Eqn 1)
B = 2C
B = 5000

A + B = 2B + 2C
; A = B + 2C = 2B = 10,000

Option C.
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I used the table format similar to the one provided by haas_mba07 above.

Try to fill in the table systematically.

We are told that
RM=5000
R=2M

When you draw the table, fill in the value for RM first (5000).

Now RM= 2M' (only mumps, not rubella)

So on the right hand side, you will write 2500.

This gives you a total for M which is 7500

Now, We are given that R=2M

So in the similar column under 5000, you will write value of R which will be 150,000

Now to get the value of R' (only rubella , not mumps) by subtracting 150,000-5000 = 10,000 (option C)

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[/quote]


hi

both = 5000
only mumps = 2500
so, mumps = 7500

now, r = 2 * 7500
= 15000

only rubella = 15000 - 5000
=10000

thanks

Imagine a two-circle Venn diagram with the following properties: left circle represents rubella, right circle represents mumps, and the intersection representing people vaccinated against both mumps and rubella.

Let "x" represent the people vaccinated against only mumps. Let "y" represent the people vaccinated against both mumps and rubella (i.e., the intersection).

You are given that the total number of people vaccinated against rubella is equal to twice the number of people vaccinated against mumps - notice that mumps includes those vaccinated against only mumps and those that are vaccinated against both mumps and rubella (i.e., x + y). So mathematically, Total rubella = 2(x+y).

You are given that 5,000 people are vaccinated against both (i.e., y = 5,000). You are also given that the number of people vaccinated against both is equal to twice the number of people vaccinated against only mumps (i.e., y = 2x). So mathematically, y = 2x and y = 5,000. From these two, x = 2,500 people vaccinated against only mumps.

Total rubella = 2(x+y); total rubella = 2(2,500+5,000) = 15,000 people vaccinated against rubella (remember this includes only rubella + rubella and mumps). But you are asked for the number of people vaccinated against only rubella. So, Total rubella = (only rubella) + (both rubella and mumps); 15,000 = (only rubella) + 5,000. So 10,000 people are vaccinated against only rubella.

Answer: C.

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.
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