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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?

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)

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

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

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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.

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 [#permalink]

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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]

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

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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.