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Teacher to Student ratio

This topic has 5 expert replies and 2 member replies
kobel51 Master | Next Rank: 500 Posts Default Avatar
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Teacher to Student ratio

Post Tue Feb 25, 2014 8:49 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P?

    1) There are 10,000 more students in School District M than there are in School District P.

    2) The ratio of the number of teachers to the number of students in School District M is 1 to 20.

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    Post Tue Feb 25, 2014 9:01 am
    To get sufficiency, we need the ratio of total student & teacher populations from one district to the next. For instance if we learn that District M has 10 times the population of district P, we'll know that M has 10 times as many students and 10 times as many teachers.

    The full solution below is taken from the GMATFix App.



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    Post Tue Feb 25, 2014 9:31 am
    kobel51 wrote:
    If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P?

    1) There are 10,000 more students in School District M than there are in School District P.

    2) The ratio of the number of teachers to the number of students in School District M is 1 to 20.
    From the stem: TM/SM = TP/SP, and we need SM/SP

    1) SM = SP + 10,000, but that leaves many possibilities. Insufficient.

    2) TM/SM = 1/20 (which also equals TP/SP). Still insufficient; TP and SP could be equal, or one or the other could be greater.

    Together: Still insufficient. You could have TM= 100, SM = 2,000 and TP=600, SP=12,000, which would give you SM/SP = 2000/12000 = 1/6. You could also have TM=1,000, SM=20,000 and TP=1500, SP = 30,000, giving you SM/SP = 20,000/30,000 = 2/3. Still insufficient.

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    Post Tue Feb 25, 2014 10:09 am
    Quote:
    If the ratio of the number of teachers to the number of
    students is the same in School District M and School
    District P, what is the ratio of the number of students
    in School District M to the number of students in
    School District P ?

    (1) There are 10,000 more students in School
    District M than there are in School District P.

    (2) The ratio of the number of teachers to the
    number of students in School District M is
    1 to 20.
    Each district has the same teacher-student ratio.
    Statement 2 implies that, in each district, the number of teachers is 1/20 of the number of students.
    The following cases satisfy BOTH statements.

    CASE 1:

    _________________P_____________M

    Students_______2000________12000

    Teachers_______100___________600

    Here, the student ratio = 2000:12000 = 1:6.

    CASE 2:

    __________________P_____________M

    Students_______10000________20000

    Teachers________500__________1000

    Here, the student ratio = 10000:20000 = 1:2.

    Since different student ratios are possible, the two statements combined are INSUFFICIENT.

    The correct answer is E.

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    jeph86 Junior | Next Rank: 30 Posts Default Avatar
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    Post Fri Sep 18, 2015 9:09 am
    because the prompt says that the ration for each district are equal, does that mean the ration student to student should be 1:1.

    DS is still confusing me!!

    Post Fri Sep 18, 2015 10:15 am
    Hi jeph86,

    The ONLY way that a ratio would be 1:1 would be if there were the same NUMBER of teachers and NUMBER of students. That is NOT what prompt states - it states that the two RATIOS (for the two Districts) is the same.

    For example, if the ratio is 1:2 in District M, then it is also 1:2 in District P. This does NOT mean that the two Districts have the same numbers of teachers and students, just the same RATIOS.

    Using this same example, District M could have 1 teacher and 2 students, while District P could have 100 teachers and 200 students (1:2 and 100:200 are the SAME RATIO) - so the specific NUMBERS involved could vary significantly.

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    jeph86 Junior | Next Rank: 30 Posts Default Avatar
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    Post Fri Sep 18, 2015 11:41 am
    Hi Rich,

    so in order for the information to be sufficient combine, district M and P should have the same ratio which be choice C instead of E?

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    Post Fri Sep 25, 2015 11:14 am
    jeph86 wrote:
    Hi Rich,

    so in order for the information to be sufficient combine, district M and P should have the same ratio which be choice C instead of E?
    Yup, you've got it!

    For instance, suppose our ratio is 3:4, which means we can write it as 3x : 4x. If we add 9 of the first thing and 12 of the second, we'll have (3x + 9) : (4x + 12), or 3(x + 3) : 4(x + 3), so our ratio stays the same!

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