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

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Manager
Joined: 05 Jul 2006
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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
13
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Difficulty:

55% (hard)

Question Stats:

69% (02:06) correct 31% (02:16) wrong based on 1065 sessions

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

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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)

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

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06 Sep 2006, 12:57
3
3
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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Re: In a certain region, the number of children who have been  [#permalink]

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06 Sep 2006, 14:27
2
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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Re: In a certain region, the number of children who have been  [#permalink]

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07 Sep 2006, 06:31
6
4
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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Re: In a certain region, the number of children who have been  [#permalink]

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08 Sep 2006, 08:34
3
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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13 Sep 2016, 17:20
1
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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21 Mar 2017, 18:30
7
1
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

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

Kudos if you agree with the explanation! Please comment if you have a better method.
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Joined: 20 Jan 2016
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Re: In a certain region, the number of children who have been  [#permalink]

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06 Nov 2017, 03:06
1
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)
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Re: In a certain region, the number of children who have been  [#permalink]

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08 Nov 2017, 16:24
1
1
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. 2,500
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.

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

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25 Nov 2017, 02:23
1
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
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Joined: 15 Jan 2017
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Re: In a certain region, the number of children who have been  [#permalink]

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11 Dec 2017, 12:20
2
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?

"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.

Kudos, please if it was useful for you
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Re: In a certain region, the number of children who have been  [#permalink]

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21 Aug 2018, 17:17
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.

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

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17 Oct 2018, 12:05
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Re: In a certain region, the number of children who have been  [#permalink]

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17 Oct 2018, 12:57
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. 2,500
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.
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Re: In a certain region, the number of children who have been  [#permalink]

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10 Jun 2019, 22:37
Solution: Given R=2M (1),
MՈR=2(M-(MՈR)) (2)
MՈR=5000 (3)
R-(MՈU)=?
From 2&3, 5000=2(M-5000) hence, M=7500 (4)
From 1 &4, R=15000
Which gives R-(MՈU)= 15000-5000=10000
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In a certain region, the number of children who have been  [#permalink]

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02 Feb 2020, 11:37
Hi everyone.

I tried to solve this question but I am still kinda struggling with how this question is written. I mean I actually don't understand the proportion here, and I don't understand why.

Let's dive into the question, how I see it:

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps.
Okay, so for mumps we have M = x, and then twice for rubella R = 2x.
The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps.
So the sum of M+R is two times more then M, so (x+2x) = 2x.

Aaand it just does not make any sense from now on. Where is the mistake I am making? How to understand those sentences?

Will appreciate help.
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Re: In a certain region, the number of children who have been  [#permalink]

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21 Jun 2020, 08:32
Answer incorrectly because of just one word - Only
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Re: In a certain region, the number of children who have been  [#permalink]

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26 Jun 2020, 23:12
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)
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Re: In a certain region, the number of children who have been   [#permalink] 26 Jun 2020, 23:12