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Need Explanation for a DS problem from OG'13

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by Digvijay01 » Wed Oct 23, 2013 12:52 pm
Hi can someone give me an explanation of why ans is "c" for this. I'm not satisfied with explanation in OG.

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.
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Source: — Data Sufficiency |

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by ceilidh.erickson » Wed Oct 23, 2013 1:30 pm
If we want the median number of employees assigned when given percents, we effectively want the 50th percentile, which would be the middle value.

Statement 1 tells us about 25% of the projects, but we can't infer anything about the others. Insufficient.

Statement 2 tells us about 35% of the projects, but again we can't infer about the others. Insufficient.

If we put the statements together:
25% of projects have 4 or more employees
35% of projects have 2 or fewer
What's the only other possibility? Exactly 3 employees. Therefore, we can infer that 40% of the projects have exactly 3 employees. If we arrange this information in order:

0%-35% is 2 or fewer
35%-75% is exactly 3
75%-100% is 4 or more

The 50% mark occurs at exactly 3 employees, so that's the median.
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by GMATGuruNY » Wed Oct 23, 2013 7:24 pm
I posted an explanation here:

https://www.beatthegmat.com/median-probl ... tml#681492
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by Uva@90 » Wed Oct 23, 2013 8:33 pm
Digvijay01 wrote:Hi can someone give me an explanation of why ans is "c" for this. I'm not satisfied with explanation in OG.

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.
Hi Digvijay01,

Firstly, how do we find the median ?
We will arrange all the number in ascending order and find the middle value.

Similarly we will approach this problem too,

arrange the project with number of employees with ascending order


0----1------------2----------------3-----------4---------------and goes on

Statement 1
25 percent of the projects at Company Z have 4 or more employees assigned to each project

so 25% have 4 or more employees

-------------------------------------------------4>----------

We dont know the rest 75 percent hence we cant decide,

Statement2
35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

so 35% have 2 or less
---------------------<2--------------------------------------------------

Combining 1 and 2

-------------------<2--------------------------4>------------------------

so, middle 40% have number of employees as 3
hence median become 3. Hence sufficient
So answer is C

Hope it is clear to you now.

Regards,
Uva.
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by Brent@GMATPrepNow » Wed Oct 23, 2013 8:56 pm
Digvijay01 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
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by Digvijay01 » Wed Oct 30, 2013 3:09 am
Thanks much...!! It sure does helped... Number line figure helped me to get more clarity.. Cheers..
Uva@90 wrote:
Digvijay01 wrote:Hi can someone give me an explanation of why ans is "c" for this. I'm not satisfied with explanation in OG.

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.
Hi Digvijay01,

Firstly, how do we find the median ?
We will arrange all the number in ascending order and find the middle value.

Similarly we will approach this problem too,

arrange the project with number of employees with ascending order


0----1------------2----------------3-----------4---------------and goes on

Statement 1
25 percent of the projects at Company Z have 4 or more employees assigned to each project

so 25% have 4 or more employees

-------------------------------------------------4>----------

We dont know the rest 75 percent hence we cant decide,

Statement2
35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

so 35% have 2 or less
---------------------<2--------------------------------------------------

Combining 1 and 2

-------------------<2--------------------------4>------------------------

so, middle 40% have number of employees as 3
hence median become 3. Hence sufficient
So answer is C

Hope it is clear to you now.

Regards,
Uva.
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