Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 05 Jul 2006
Posts: 178

In a certain region, the number of children who have been
[#permalink]
Show Tags
06 Sep 2006, 12:15
Question Stats:
67% (02:07) correct 33% (02:19) wrong based on 880 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
13 Sep 2016, 23:05
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)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Director
Joined: 02 Jun 2006
Posts: 915

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
06 Sep 2006, 15:42
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)
Attachments
Rubella.JPG [ 12.38 KiB  Viewed 50885 times ]




Director
Joined: 02 Jun 2006
Posts: 915

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
06 Sep 2006, 13:57
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



Retired Moderator
Joined: 05 Jul 2006
Posts: 1380

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
06 Sep 2006, 15:27
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)



SVP
Joined: 20 Nov 2005
Posts: 2095
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD  Class of 2008

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
07 Sep 2006, 07:31
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
_________________
SAID BUSINESS SCHOOL, OXFORD  MBA CLASS OF 2008



Manager
Joined: 27 Jul 2006
Posts: 227

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
08 Sep 2006, 09:34
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



Manager
Joined: 17 Jun 2015
Posts: 191
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
13 Sep 2016, 18:20
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.
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Manager
Joined: 13 Dec 2013
Posts: 142
Location: United States (NY)
Concentration: General Management, International Business
GMAT 1: 710 Q46 V41 GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
21 Mar 2017, 19:30
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.



Manager
Joined: 20 Jan 2016
Posts: 174

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
06 Nov 2017, 04:06
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)



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
08 Nov 2017, 17:24
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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 265

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
25 Nov 2017, 03:23
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



Senior Manager
Joined: 15 Jan 2017
Posts: 332

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
11 Dec 2017, 13:20
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



Intern
Joined: 19 Jul 2018
Posts: 2

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
21 Aug 2018, 18:17
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.



Manager
Joined: 24 Sep 2018
Posts: 136

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
17 Oct 2018, 13:05
Attachment:
Screen Shot 20181018 at 1.34.49 AM.png [ 36.11 KiB  Viewed 15158 times ]



GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
17 Oct 2018, 13:57
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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



Intern
Joined: 13 Jan 2017
Posts: 8
Location: India
GMAT 1: 550 Q50 V16 GMAT 2: 680 Q49 V33
GPA: 2.92

Re: In a certain region, the number of children who have been
[#permalink]
Show Tags
10 Jun 2019, 23:37
Solution: Given R=2M (1), MՈR=2(M(MՈR)) (2) MՈR=5000 (3) R(MՈU)=? From 2&3, 5000=2(M5000) hence, M=7500 (4) From 1 &4, R=15000 Which gives R(MՈU)= 150005000=10000 Correct Answer is C.




Re: In a certain region, the number of children who have been
[#permalink]
10 Jun 2019, 23:37






