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rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

by rintoo22 » Sat Mar 23, 2013 12:04 pm

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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

I got the answer correct, C. However I am not satisfied with the way I arrived to the answer. Going throught the problem again, I reckon correct answer should be E. The expalantion is as follows

25% Projects- 4 or more employees
35% Projects- 2 or less employees
We are left with 40% Projects (which is the biggest chunk). Given that no information is given regarding this, I reckon both the above statements are in- sufficient.
Please assist.

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Source: Beat The GMAT — Data Sufficiency | Sat Mar 23, 2013 12:04 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Sat Mar 23, 2013 12:22 pm

A. 25% have >=4 employees we don't know anything about the other 75% so insufficient
B. 35% have <=2 employees we don't know anything about other 65%

together we know 35% has either 1 or 2 employees per project and 25% has 4 or more employees per project. that means 100 - 25 - 35 or 40% has 3 employees per project.
clearly median = 3 hence sufficient.

Also if you can visualize on a number line, median is what comes at 50%. first 35% (1-35 on number line) is <=2, top 25 is >=4 (or 75-100 on number line is >=4). the middle portion on the number line on which 50 (median) lies = 3 employees per project.

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rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

by rintoo22 » Sat Mar 23, 2013 12:30 pm

Thanks for the response. I get your point.
A. 25% have >=4 employees we don't know anything about the other 75% so insufficient
B. 35% have <=2 employees we don't know anything about other 65%

So ideally we are left with '3'.

Thanks Once again.

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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 » Sun Mar 24, 2013 6:01 am

rintoo22 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.

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

Brent Hanneson - Creator of GMATPrepNow.com

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