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Median Problem

This topic has 3 expert replies and 1 member reply
ygdrasil24 Senior | Next Rank: 100 Posts
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Median Problem

Post Sun Jun 30, 2013 5:13 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the median number of employees assigned per project for the projects at Company Z ?
    (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
    (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

    Getting lost..please post some good solution.

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    Post Sun Jun 30, 2013 7:40 am
    ygdrasil24 wrote:
    What is the median number of employees assigned per project for the projects at Company Z ?
    (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
    (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

    Getting lost..please post some good solution.
    In ascending order of EMPLOYEES PER PROJECT, let the projects be numbered 1 through 100:
    1, 2, 3.....49, 50, 51, ....98, 99, 100.
    Projects 50 and 51 determine the MEDIAN number of employees:

    Question rephrased: How many employees are assigned to PROJECTS 50 and 51?

    Looking at the two statements, we should note that there are 3 options:
    Option A: A project is assigned 2 OR FEWER employees.
    Option B: A project is assigned EXACTLY 3 employees.
    Option C: A project is assigned 4 OR MORE employees.

    Neither statement alone is sufficient to determine the number of employees assigned to projects 50 and 51.
    Statements combined:
    According to statement 2, Projects 1 through 35 -- the BOTTOM 35 projects -- conform to OPTION A.
    According to statement 1, Projects 76 through 100 -- the TOP 25 projects -- conform to OPTION C.
    Implication:
    Projects 36-75 -- the MIDDLE 40 projects -- conform to OPTION B.

    Thus, Projects 50 and 51 are each assigned EXACTLY 3 employees, implying that the median number of employees per project = 3.
    SUFFICIENT.

    The correct answer is C.

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    Last edited by GMATGuruNY on Wed Oct 23, 2013 7:23 pm; edited 1 time in total

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    Post Sun Jun 30, 2013 7:49 am
    ygdrasil24 wrote:
    What is the median number of employees assigned per project for the projects at Company Z ?
    (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
    (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

    Getting lost..please post some good solution.
    Target question: What is the median number of employees assigned per project?

    Statement 1: 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
    Let's pretend that there are 4 projects altogether.
    There are several sets of values that meet this condition. Here are two:
    Case a: the set of numbers representing employees per project are {1, 1, 1, 4} in which case the median is 1
    Case b: the set of numbers representing employees per project are {2, 2, 2, 4} in which case the median is 2
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 1: 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.
    Using logic similar to the above, we can show that statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined:
    35% projects have 2 employees or fewer, and 25% of the projects have 4 employees or more. So, 40% projects have exactly 3 employees.

    This tells us that the median must be 3.
    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer = C

    Cheers,
    Brent

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    ygdrasil24 Senior | Next Rank: 100 Posts
    Joined
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    Posted:
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    Post Sun Jun 30, 2013 9:52 am
    Thank you! Do you think its a 700+ question ?

    Post Sun Jun 30, 2013 10:35 pm
    ygdrasil24 wrote:
    Thank you! Do you think its a 700+ question ?
    I'd rate this as a 650 - 700 question.

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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