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

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In a certain region, the number of children who have been [#permalink]

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06 Sep 2006, 11:15
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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. 2,5000
B. 7,500
C. 10,000
D. 15,000
E. 17,500
[Reveal] Spoiler: OA
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06 Sep 2006, 12:57
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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

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06 Sep 2006, 14:27
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Folks i tried to solve it using venn diagrams still cant get it

I will appreciate any explanation that is not based on a formula that i have to revise( am ver bad at revising formulas)
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06 Sep 2006, 14:42
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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

yezz wrote:
Folks i tried to solve it using venn diagrams still cant get it

I will appreciate any explanation that is not based on a formula that i have to revise( am ver bad at revising formulas)

Attachments

Rubella.JPG [ 12.38 KiB | Viewed 20562 times ]

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07 Sep 2006, 06:31
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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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08 Sep 2006, 08:34
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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
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Re: In a certain region, the number of children who have been [#permalink]

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26 Mar 2014, 05:56
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Re: In a certain region, the number of children who have been [#permalink]

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28 Mar 2015, 10:20
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Re: In a certain region, the number of children who have been [#permalink]

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24 Apr 2016, 11:30
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Re: In a certain region, the number of children who have been [#permalink]

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13 Sep 2016, 17:20
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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Re: In a certain region, the number of children who have been [#permalink]

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13 Sep 2016, 22:05
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lan583 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. 2,5000
B. 7,500
C. 10,000
D. 15,000
E. 17,500

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

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Re: In a certain region, the number of children who have been   [#permalink] 13 Sep 2016, 22:05
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