Ann, Beth, and Steve each spent some amount of time

Question

Ann, Beth, and Steve each spent some amount of time on a certain project last week. If the average (arithmetic mean) amount of time that the 3 people spent on the project last week was 15 hours per person, what was the median amount?

(1) Last week Ann and Beth spent a total of 30 hours on the project
(2) Last week Steve spent 15 hours on the project

https://gmatclub.com/forum/download/file.php?id=78675

Bunuel · Accepted Answer

Ann, Beth, and Steve each spent some amount of time on a certain project last week. If the average (arithmetic mean) amount of time that the 3 people spent on the project last week was 15 hours per person, what was the median amount?

Given that A + B + S = 15 * 3 = 45, we are asked to find the median of {A, B, S}.
 
(1) Last week Ann and Beth spent a total of 30 hours on the project

This means A + B = 30, making S equal to 15, which is the average. Since both A and B cannot be less than the average or both cannot be more than the average, we would have one of the following two cases: A ≤ 15 ≤ B or B ≤ 15 ≤ A. Thus, the median, the middle value, is 15. Sufficient.

(2) Last week Steve spent 15 hours on the project

This directly gives S = 15, which makes this statement sufficient by the same logic as above.

Answer: D.

P.S. Can you please post a screenshot of the question? That would be very helpful. Thank you.

vaishmahe · Answer

The question is from GMAT Official Mock 4

Bunuel · Answer

__________________ Thank you!

mirfan07 · Answer

But what if the time given in hours be taken in decimals?? Just a concern, would that be usually mentioned??

vanacore · Answer

why cant they have 1;29;15 hours?

Bunuel · Answer

The median of {1, 15, 29} is still 15.

ManifestDreamMBA · Answer

Avg Time = 15
OR
Total Time = 15*3 = 45

Statement 1
A+B = 30
Which means S = 15
A and B can be split in multiple ways but 15 from S will always be the median
For e.g. 
If A=B = 15, then 15,15,15 => 15 is the median
If A=1,B = 29, then 1,15,29 => 15 is the median
If A=15.5,B = 14.5, then 14.5,15,16.5 => 15 is the median
Sufficient

Statement 2
S = 15
This means A+B = 30
This is the exact same information we have from 1 and can solve similarly to find the median
Sufficient

bumpbot · Answer

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Ann, Beth, and Steve each spent some amount of time

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