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college T

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college T

Post Wed Jun 22, 2016 10:11 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Of the 200 students at college T majoring in one or more of the science, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number of students majoring in both chemistry and biology could be any number from

    A) 20 to 50

    B) 40 to 70

    C) 50 to 130

    D) 110 to 130

    E) 110 to 150

    OAD

    Please explain why not E?

    Why 130 is the maximum?

    Thanks in advance.

    Kavin

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    Post Wed Jun 22, 2016 10:20 am
    There are some nice solutions here: http://qa.www.beatthegmat.com/group-problem-t282407.html

    Cheers,
    Brent

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    Post Wed Jun 22, 2016 8:38 pm
    Hi Kavin,

    This question can be solved rather handily with the Tic-Tac-Toe board, but you can also use the Overlapping Sets Formula here (although it won't be applicable on every Overlapping Sets question that you might see on Test Day).

    This prompt comes with a couple of 'twists' to it:
    1) The number of students who study 'neither' is NOT a fixed value - it's a range.
    2) The question asks for the RANGE of students who could study both Chemistry and Biology.

    Here's how you can use the Formula though...

    Total = Gp.1 + Gp.2 - Both + Neither

    200 = 130 + 150 - B + (>=30)
    200 = 280 - B + (>=30)
    200 = (>=310) - B
    B = >=110

    This gives you the 'lower end' of the range, but does not immediately give you the 'upper end.' To find that, you have to think about the numbers involved. Since 130 students study Chemistry and 150 study Biology, the MAXIMUM number who could study both would be 130 (and that's if EVERY Chemistry student also studied Biology). Thus, the range is 110 to 130, inclusive.

    Final Answer: D

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    Post Thu Jun 23, 2016 3:53 pm
    You'd have the maximum overlap if everyone in the less populated major is also in the more populated major: if every chem major is a bio major.

    You'd have the minimum overlap if you have the fewest possible people in neither major: if you have exactly 30 who aren't majoring in chem or bio.

    In the first case we have 130 in both, 20 only in bio, and 50 in neither.

    In the second case, we have 30 in neither, leaving (130 + 150 - Overlap) = 170, or Overlap = 110.

    That gives us our range: 110 to 130.

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    Post Thu Jun 23, 2016 3:54 pm
    Needgmat wrote:
    Please explain why not E?

    Why 130 is the maximum?

    Thanks in advance.
    This is a great question! If you had 150 students in both, the overlap (150) would be MORE than the number of students in biology at all (130). But the overlap (dual major) is a SUBSET of the number of students in biology at all, so 130 ≥ Overlap.

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