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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?

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)

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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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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