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In a certain region, the number of children who have been
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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. 2,500 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
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13 Sep 2016, 22:05
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 Answer (C)
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Re: In a certain region, the number of children who have been
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06 Sep 2006, 14:42
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
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06 Sep 2006, 12:57
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



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Re: In a certain region, the number of children who have been
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06 Sep 2006, 14:27
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
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07 Sep 2006, 06:31
C
Make Venn Diagram.
Mumps = x
Rubella = 2x
Both = y
Only Mumps = xy
As given y = 2(xy)
i.e 3y = 2x
y = 5000
therefore x = 7500
Only Rubella = 2xy = 2*7500  5000 = 10000
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Re: In a certain region, the number of children who have been
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08 Sep 2006, 08:34
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
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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
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21 Mar 2017, 18:30
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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Re: In a certain region, the number of children who have been
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06 Nov 2017, 03:06
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 150,0005000 = 10,000 (option C)



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Re: In a certain region, the number of children who have been
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08 Nov 2017, 16:24
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. Answer: C
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Re: In a certain region, the number of children who have been
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25 Nov 2017, 02:23
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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Re: In a certain region, the number of children who have been
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11 Dec 2017, 12:20
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
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21 Aug 2018, 17:17
Imagine a twocircle 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.



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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
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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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