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Need better explanation: Statistics OG13 Question# 139

This topic has 3 expert replies and 3 member replies
tanvis1120 Senior | Next Rank: 100 Posts
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Need better explanation: Statistics OG13 Question# 139

Post Wed Jul 23, 2014 3:25 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Q. What is the median number of employees assigned per project for the projects at company Z?
    1. 25% of the projects at company Z have 4 or more employees assigned to each project.
    2. 35% of the projects at company Z have 2 or fewer employees assigned to each project.

    My answer is E.
    Explanation:
    Let the total number of projects be 100.

    St 1: 25% or 25 projects have 4 or more employees. Here, we have no idea about the highest threshold of employees (>4 can 5 or 20 etc.). Also, what about the remaining 75 project? So, the median cannot be calculated. (Not Sufficient)

    St 2: 35% or 35 projects have 2 or fewer employees.
    We cannot determine the median from this.
    35 projects can have different number of employees,2 or 1.
    What about the remaining 65? (Not Sufficient)

    St1 + St2: 100-(25+35) = 40 projects. We have no idea about the number of employees that each of the remaining project has. (Not Sufficient)

    OG13 says that the correct answer is C (Calculated median is 3). But I am having hard time understanding their explanation.

    If your answer is C too, please explain it to me clearly.

    Thank You in Advance !

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    Post Wed Jul 23, 2014 3:28 pm
    tanvis1120 wrote:
    What is the median number of employees assigned per project for the projects at company Z?
    1) 25% of the projects at company Z have 4 or more employees assigned to each project.
    2) 35% of the projects at company Z have 2 or fewer employees assigned to each project.

    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 2: 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.

    To find the median, we must find the middlemost value when all of the values are listed in ASCENDING order.
    So, the first 35% of the numbers will be 1's and 2's.
    Then next 40% of the numbers will be 3's
    And the last 25% of the numbers will be 4, 5's, etc

    As you can see, the MIDDLEMOST value will be 3. In other words, 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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    Post Wed Jul 23, 2014 3:36 pm
    tanvis1120 wrote:
    Q. What is the median number of employees assigned per project for the projects at company Z?
    1. 25% of the projects at company Z have 4 or more employees assigned to each project.
    2. 35% of the projects at company Z have 2 or fewer employees assigned to each project.

    My answer is E.
    Explanation:
    Let the total number of projects be 100.

    St 1: 25% or 25 projects have 4 or more employees. Here, we have no idea about the highest threshold of employees (>4 can 5 or 20 etc.). Also, what about the remaining 75 project? So, the median cannot be calculated. (Not Sufficient)

    St 2: 35% or 35 projects have 2 or fewer employees.
    We cannot determine the median from this.
    35 projects can have different number of employees,2 or 1.
    What about the remaining 65? (Not Sufficient)

    St1 + St2: 100-(25+35) = 40 projects. We have no idea about the number of employees that each of the remaining project has. (Not Sufficient)

    OG13 says that the correct answer is C (Calculated median is 3). But I am having hard time understanding their explanation.

    If your answer is C too, please explain it to me clearly.

    Thank You in Advance !
    I've highlighted the problem above.
    Statement 1 accounts for projects with 4 or more employees
    Statement 2 accounts for projects with 2 or fewer employees
    The remaining 40% of projects must have 3 employees

    Cheers,
    Brent

    _________________
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    tanvis1120 Senior | Next Rank: 100 Posts
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    Post Wed Jul 23, 2014 3:44 pm
    Ohhh...
    I got the target question totally wrong!!!
    I got it now.. I was thinking in an entirely different path, something weird !!!
    Thanks !

    Post Wed Jul 23, 2014 4:26 pm
    tanvis1120 wrote:
    Ohhh...
    I got the target question totally wrong!!!
    I got it now.. I was thinking in an entirely different path, something weird !!!
    Thanks !
    If you read the target question as asking for the mean (and not the median), then the correct answer would, indeed, be E

    Cheers,
    Brent

    _________________
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    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!

    Top Member

    Post Thu Jul 24, 2014 12:48 am
    tanvis1120 wrote:
    Q. What is the median number of employees assigned per project for the projects at company Z?
    1. 25% of the projects at company Z have 4 or more employees assigned to each project.
    2. 35% of the projects at company Z have 2 or fewer employees assigned to each project.

    CONCEPT : Median is the middle term of the set when terms are arranged in ascending/descending order.
    If the number of terms is even in the set then the average of two middle terms of the set is called median


    Let, there are 100 projects in the set which according to Descending order of assigned number of employees is represented as {1, 2, 3, .....34, 35, 36, 37.......98, 99, 100}

    Since the number of terms in the set is even therefore the Median number of Employees assigned will be the Average of No of employees assigned to 50th and 51st Project

    Statement 1) 25% of the projects at company Z have 4 or more employees assigned to each project.

    {1, 2, 3, .....24, 25, 26, 27.......98, 99, 100}
    i.e. Red Projects are representing the number of employees 4 or more in descending order

    The number of employees assigned to 50th ans 51st project are unknown therefore,
    INSUFFICIENT

    Statement 2)35% of the projects at company Z have 2 or fewer employees assigned to each project.
    {1, 2, 3, .....24, 25,...... 66, 67.......98, 99, 100}
    i.e. Blue Projects are representing the number of employees 4 or more in descending order

    The number of employees assigned to 50th ans 51st project are unknown therefore,
    INSUFFICIENT

    Combining the two statements

    {1, 2, 3, .....24, 25,26, 27......64, 65, 66, 67.......98, 99, 100}

    Since Red are representing equal to or Greater than 4 employees and Blue are representing lesser than or equal to 2 employees projects then remaining projects must have employees between 2 and 4
    i.e. number of employees for Black projects = 3

    i.e. 50th and 51st project have 3 emloyees each.
    i.e. Median Number of employees - 3

    Answer: Option C

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    tanvis1120 Senior | Next Rank: 100 Posts
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    Post Thu Jul 24, 2014 11:10 am
    Thanks.. Nice explanation!

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