Need better explanation: Statistics OG13 Question# 139

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tanvis1120: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sat Dec 28, 2013 8:53 amFollowed by: 5 members; Location: United States; Thanked: 2 times

by tanvis1120 » Wed Jul 23, 2014 3:25 pm

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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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Source: Beat The GMAT — Data Sufficiency | Wed Jul 23, 2014 3:25 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » 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

Brent Hanneson - Creator of GMATPrepNow.com

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by Brent@GMATPrepNow » 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

Brent Hanneson - Creator of GMATPrepNow.com

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tanvis1120: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Sat Dec 28, 2013 8:53 amFollowed by: 5 members; Location: United States; Thanked: 2 times

by tanvis1120 » 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 !

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » 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

Brent Hanneson - Creator of GMATPrepNow.com

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » 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; Posts: 95; Joined: Sat Dec 28, 2013 8:53 amFollowed by: 5 members; Location: United States; Thanked: 2 times

by tanvis1120 » Thu Jul 24, 2014 11:10 am

Thanks.. Nice explanation!

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