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Vaccinated Against Rubella

This topic has 3 expert replies and 1 member reply
bml1105 Master | Next Rank: 500 Posts
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Vaccinated Against Rubella

Post Tue Jun 03, 2014 2:29 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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


    OA: C

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    Post Tue Jun 03, 2014 6:54 pm
    Quote:
    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 5000 have been vaccinated against both, how many have been vaccinated only against rubella?

    2500 : 7500 : 10000 : 15000 : 17500
    This is an EITHER/OR group problem.
    Every child EITHER has been vaccinated against mumps OR has not.
    Every child EITHER has been vaccinated against rubella OR has not.
    For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.

    Let M = mumps, NM = not mumps, R = rubella, NR = not rubella.
    In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.

    The number who have been vaccinated against both is twice the number of who have been vaccinated against only mumps:
    ttp://postimg.org/image/9ljfassxd/" target="_blank">

    The number who have been vaccinated against rubella is twice the number who have been vaccinated against mumps:
    ttp://postimg.org/image/6gvritix3/" target="_blank">

    5000 have been vaccinated against both:
    According to the grid, both = 2x = 5000 and only rubella = 4x = 10,000.

    The correct answer is C.

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    GyanOne Master | Next Rank: 500 Posts
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    Post Wed Jun 04, 2014 6:23 am
    From the question statement, we can surmise:

    Number vaccinated against both = 5000
    Number vaccinated only against Mumps = 2500

    Number vaccinated against mumps = Number vaccinated only against mumps + Number vaccinated against both = 5000 + 2500 = 7500

    Number vaccinated against Rubella = 2 * 7500 = 15000

    Number vaccinated against only Rubella = Number vaccinated against Rubella - Number vaccinated against both = 15000 - 5000 = 10,000

    Option (C).

    Post Wed Jun 04, 2014 7:13 am
    I thought I'd point out that Mitch's "group grid" (aka Double Matrix Method) can be used for most questions featuring a population in which each member has two characteristics associated with it.
    Here, we have a population of children, and the two characteristics are:
    - vaccinated against mumps or not vaccinated against mumps
    - vaccinated against rubella or not vaccinated against rubella

    This question type is VERY COMMON on the GMAT, so be sure to master the technique.

    To learn more about the Double Matrix Method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Once you’re familiar with this technique, you can attempt these additional practice questions:

    Easy Problem Solving questions
    - http://www.beatthegmat.com/the-aam-aadmi-party-t272242.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html

    Medium Problem Solving questions
    - http://www.beatthegmat.com/probability-question-t273360.html
    - http://www.beatthegmat.com/posted-speed-limit-t272374.html
    - http://www.beatthegmat.com/motel-t271938.html
    - http://www.beatthegmat.com/of-the-applicants-passes-a-certain-test-15-t270255.html
    - http://www.beatthegmat.com/opening-night-and-late-patrons-t264869.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html

    Difficult Problem Solving questions
    - http://www.beatthegmat.com/ratio-problem-t268339.html
    - http://www.beatthegmat.com/overlapping-sets-question-t265223.html
    - http://www.beatthegmat.com/fractions-t264254.html
    - http://www.beatthegmat.com/overlapping-sets-t264092.html
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2

    Easy Data Sufficiency questions
    - http://www.beatthegmat.com/for-what-percent-of-those-tested-for-a-certain-t270596.html
    - http://www.beatthegmat.com/ds-quest-t187706.html

    Medium Data Sufficiency questions
    - http://www.beatthegmat.com/sets-matrix-ds-t271914.html
    - http://www.beatthegmat.com/each-of-people-voted-once-in-an-election-x-t271375.html
    - http://www.beatthegmat.com/a-manufacturer-t270331.html
    - http://www.beatthegmat.com/in-costume-for-halloween-t269355.html
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1

    Difficult Data Sufficiency questions
    - http://www.beatthegmat.com/double-set-matrix-question-t271423.html
    - http://www.beatthegmat.com/sets-t269449.html
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3

    Cheers,
    Brent

    _________________
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    Post Wed Nov 08, 2017 4:25 pm
    bml1105 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

    _________________
    Jeffrey Miller Head of GMAT Instruction

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