In a certain region, the number of children who have been

Question

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

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

KarishmaB · Accepted Answer

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)

haas_mba07 · Answer

Mt = Number vaccinated against Mumps
x = Number vaccinated against Mumps but not Rubella

Looking at the attached figure, if the number of Rubella and not mumps vaccinated is 5000 *( which is 2x) then x = 2500 which is the number vaccinated against Mumps but not Rubella.

Total vaccinated against Mumps = 7500

Total vaccinated against Rubella = 2 x Mt = 15000

Therefore, total Rubella but not Mumps vaccinated = 15000 - 5000 = 10, 000

ps_dahiya · Answer

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

haas_mba07 · Answer

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

defenestrate · Answer

We know that 5000 people have both MR vac.

We know that 2500 people have only M

Total people with M vac is 7500

we know that total R=2M
15000
we also know that 5000 people have both MR
15000
-5000
=10000

hdwnkr · Answer

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.

Cez005 · Answer

Number vaccinated against both: 5,000. 
The number vaccinated against both is twice the number vaccinated only against mumps. Number vaccinated only against mumps = 5000/2=2500.
Number vaccinated against mumps = 7500
Number vaccinated against rubella = 5000 + n
5000+n=2*7500
5000+n=15000
n=10000

JeffTargetTestPrep · Answer

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

testcracker · Answer

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

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

hi

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

now, r = 2 * 7500
= 15000

only rubella = 15000 - 5000
=10000

thanks

Madhavi1990 · Answer

Did it mostly like a word 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 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

" In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps."  --> mumps = x, rubella = 2x

" The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps.  " - both would mean 2x +x = 3x have been vaxxed against both. So twice of this => 3x = 2x of mumps => 3x - 2x =0, x = 1 both, as per question. Thus mumps and 'both' are the same.

"If 5,000 have been vaccinated against both, how many have been vaccinated only against rubella?" --> says that x = 5000. So rubella, as per earlier, is 10,000.

GMATYoda · Answer

Screen Shot 2018-10-18 at 1.34.49 AM.png

fskilnik · Answer

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!)

https://preview.ibb.co/kESBo0/17-Oct18-6h.gif

? = 4k

2k = 5,000\,\,\,\, \Rightarrow \,\,\,\,? = 10,000

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

NishantR · Answer

This is  a super simple question  once you break it down.

Step 1 draw a Venn diagram with 5 data points and ensure to either use capital R, M, B & small r, m or R, M, B, x & y. You will understand the reason in a bit
1. R = the  TOTAL  number of children who have been vaccinated against rubella
2. r = the number of children who have been vaccinated against rubella  ONLY 
3. M = the  TOTAL  number of children who have been vaccinated against mumps
4. m = the number of children who have been vaccinated against rubella  ONLY 
5. B = Child that have been vaccinated for both

So we know 
1. r = R-B
2. R = 2M
3. M = B+m
4. m = B/2
5. B = 5000

Now just work backwards from 5,4,3,2,1 and you are done
5. B = 5000
4. m = 5000/2 
 >m = 2500
3. M = B+m
 >M = 5000 + 2500
 >M = 7500
2. R = 2M
 >R = 2(7500)
 >R = 15000
1. r = R-B
 >r=15000-5000
 >r=10000

And you reach the answer.... simple question once you look at it correctly and daw the Venn diagram out...

Once you see the Venn diagrams you can see that r= 2B (since B = 5000, r = 10,000)

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=ub6nqvtlY-w

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83171 Harsha GMAT-Club-Forum-saibqhsb.png

Nidhibatra · Answer

WHERE IS IT WRITTEN IN 2ND LINE THAT WE ARE TALKNG ONLY ABOUT MUMPS BECAUSE IT SAYS The number who have been vaccinated against both is twice
the number who have been vaccinated against mumps.It doesnt mention "only mumps"

Bunuel · Answer

Read carefully:

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

Shreya0308 · Answer

Hi, I had a doubt while solving this question. When calculating the value for  only mumps , you subtracted  x − y . How did you know that in the first statement —  “the number vaccinated against rubella is twice the number vaccinated against mumps”  — the term  mumps  includes those who were vaccinated for  both  diseases as well?
I interpreted it as referring only to  mumps alone  (excluding those vaccinated for both), which is why I used  y − x  instead.

In a certain region, the number of children who have been

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