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jjf Just gettin' started! Default Avatar
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Ratios Question Post Mon Dec 13, 2010 5:22 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B?

    A) 29/12
    B) 59/10
    C) 65/8
    D) 48/5
    E) 29/3

    I had a difficult time with this question on a Kaplan CAT. The explanation given was not great.

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    Post Mon Dec 13, 2010 6:25 pm
    jjf wrote:
    The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B?

    A) 29/12
    B) 59/10
    C) 65/8
    D) 48/5
    E) 29/3

    I had a difficult time with this question on a Kaplan CAT. The explanation given was not great.
    This is a weighted average question.

    (4/9)A = juniors in A
    (3/20)B = juniors in B
    (5/12)(A+B) = juniors in A+B combined

    Since (juniors in A) + (juniors in B) = (juniors in A+B), we can set up the following equation:

    (4/9)A + (3/20)B = (5/12)(A+B)
    (80/180)A + (27/180)B = (75/180)(A+B)
    80A + 27B = 75A + 75B
    5A = 48B
    A/B = 48/5

    The correct answer is D.

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    Post Mon Dec 13, 2010 6:34 pm
    GMATGuruNY wrote:
    jjf wrote:
    The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B?

    A) 29/12
    B) 59/10
    C) 65/8
    D) 48/5
    E) 29/3

    I had a difficult time with this question on a Kaplan CAT. The explanation given was not great.
    This is a weighted average question.

    (4/9)A = juniors in A
    (3/20)B = juniors in B
    (5/12)(A+B) = juniors in A+B combined

    Since (juniors in A) + (juniors in B) = (juniors in A+B), we can set up the following equation:

    (4/9)A + (3/20)B = (5/12)(A+B)
    (80/180)A + (27/180)B = (75/180)(A+B)
    80A + 27B = 75A + 75B
    5A = 48B
    A/B = 48/5

    The correct answer is D.
    It's Great to see the solution, Can we also find the minimum value for the Number of students in Class A and Class B, I know problem is solved but is it possible to find the minimum integral value for A and B, considering all the situations,

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    shayam Just gettin' started! Default Avatar
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    Post Sun May 15, 2011 12:55 pm
    Solution using Allegation Approach

    Junior in A..............Juniors in B

    4/9.............M=5/12...........3/20

    Using Allegation Approach:
    Ratio of a:b = B-M/M-A

    Hence a:b = (3/20 -5/12) / (5/12 -4/9)

    = 48:5 Choice D

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