Data Sufficiency

Spent 1h and still no clue... Any help greatly appreciated!

Six people raced together. If the gold medal winner finished the race in 15 minutes, and no any two athletes finished the race in the same time, did the silver medal winner finish the race in less than 15 minutes and 40 seconds?

1). The average time they cost was 16 minute.

2). The last one TOOK 18 minutes, the silver winner TOOK 1MIN AND 21 SEC less than the fifth one , and the third one is one second quicker than the fourth one.

Answer is C:

1. It says that the mean is 16 , this is not sufficient to conclude anything about the second place.
2. This gives information that the last one took 18 min and the 3 & 4 th are almost the same time.
- insufficient

But now we can combine both of the statement. I would recommend you draw a time line
15---------16--------------18
The above time line is showing the first and the last alsong with the median time.
We notice that first one is 1 min less than mean and last one is 2 min more than mean.

Therefore the difference(gain) is 2 min - 1 min = 1min, which has to be compensated between the other 4 people.

Now I will take a value to test whether having the second one as 15.40 is possible to compensate for the gain.
16-15.40 = 20 sec will be compensated. Still 40 sec needs to be comensated . Even if we take 3 and 4 near to 2
We wont be able to make it possible. Also person 5 cant be on the left hand side of mean as difference between
2 and 5 is 1.21

From the above experiment we conclude that the second person completed race within 15.40 second.


I am sure there would be an easier way to explain this.

Cheers,

thanks a lot!

another possible solution:


15+x+y+(y+1s)+(x+1m21s)+18=96

if we assume silver winner took 15m40s:

15+15m40s+y+(y+1s)+17m1s+18=96

2y=30m18s
y=15m9s so according to this 3rd place finished faster than second, therefore, second place must have finished faster than in 15m40s

that's great explanation! many thanks!