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A certain high school (OG13)

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alex.gellatly Master | Next Rank: 500 Posts Default Avatar
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A certain high school (OG13)

Post Thu Aug 02, 2012 9:45 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A certain high school with a total enrollment of
    900 students held a science fair for three days last
    week. How many of the students enrolled in the high
    school attended the science fair on all three days?
    (1) Of the students enrolled in the school,
    30 percent attended the science fair on two
    or more days.
    (2) Of the students enrolled in the school,
    10 percent of those that attended the science
    fair on at least one day attended on all three
    days.

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    Anurag@Gurome GMAT Instructor
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    Post Thu Aug 02, 2012 9:59 pm
    alex.gellatly wrote:
    A certain high school with a total enrollment of
    900 students held a science fair for three days last
    week. How many of the students enrolled in the high
    school attended the science fair on all three days?
    (1) Of the students enrolled in the school,
    30 percent attended the science fair on two
    or more days.
    (2) Of the students enrolled in the school,
    10 percent of those that attended the science
    fair on at least one day attended on all three
    days.
    According to the given information, there can be number of students, who didn't attended the fair.

    So, following cases can be possible:

    A. Students who attended on only one day
    B. Students who attended on two days exactly
    C. Students who attended on all three days
    D. Students who did not attended the fair

    So, A + B + C + D = 900. We have to find C.

    (1) 30% of 900 attended 2 or more days implies 0.30 * 900 = 270 attended 2 or more days.
    B + C = 270; Not SUFFICIENT.

    (2) 10 percent of those that attended the science fair on at least one day attended on all three days implies 10% * (A + B + C)= C
    A + B = 9C; Not SUFFICIENT.

    Combining (1) and (2), B + C = 270, A + B = 9C and A + B + C + D = 900.
    We have 3 equations, 4 unknowns; Not SUFFICIENT.

    The correct answer is E.

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