I have an elimination based approach, here goes:

Let the pieces be a1, a2, a3, a4, a5.
We know that:
- n = 5
- Mean = 124
- a3 = 140
- a4, a5 are at least 140
- a1 + a2 + a3 + a4 + a5 = 124*5 = 620
- a1 + a2 + a4 + a5 = 620 - a3 = 480


First, strike off choices 130 and 140, otherwise mean can never be 124.

Now, consider a1 = 110.
This implies, a2 + a4 + a5 = 480 - a1 = 480 - 110 = 370.
If a4 and a5 are at least 140 each, then a4+a5 is at aleast 280.
This impiles, a2 is at most 370 - 280 = 90. This cannot be true since a1 is 110.
So strike off choice 110.

Now, consider a1 = 100.
This impiles a2 is at most 480 - 100 - 280 = 100.
This makes sense, as the Mean also checks out.

Perhaps someone can propose a better solution.

Other Approach:

Information Provided:
Total Length of 5 Pieces - 124 * 5 = 620
Median = 140 (Third piece in row ordered by length)

So if median is 140 then maximum of 3 pieces could be of length 140 and 2 could be pieces of shortest length.

140 * 3 = 420

Once you have this value (420), subtract it from 620 so we are left with 200 for rest 2 spots.

Divide 200 by 2, 100.

Its an alternative approach, I found it quick.
Hope that helps!

albertrahul wrote:Other Approach:

Information Provided:
Total Length of 5 Pieces - 124 * 5 = 620
Median = 140 (Third piece in row ordered by length)

So if median is 140 then maximum of 3 pieces could be of length 140 and 2 could be pieces of shortest length.

140 * 3 = 420

Once you have this value (420), subtract it from 620 so we are left with 200 for rest 2 spots.

Divide 200 by 2, 100.

Its an alternative approach, I found it quick.
Hope that helps!

Hi, Albertrahul!
Can you explane, why you devide 200 by 2?

The fact is that I've used the same approach in my solution. But I was confused with the last operation (when you devide 200 by 2). Don't you think that the first and the second terms in the set might be 90 and 110, respectively? In this case, the least number would be 90...
According to the right aswer, I am wrong... I just can't understand why

olika wrote:

albertrahul wrote:Other Approach:

Information Provided:
Total Length of 5 Pieces - 124 * 5 = 620
Median = 140 (Third piece in row ordered by length)

So if median is 140 then maximum of 3 pieces could be of length 140 and 2 could be pieces of shortest length.

140 * 3 = 420

Once you have this value (420), subtract it from 620 so we are left with 200 for rest 2 spots.

Divide 200 by 2, 100.

Its an alternative approach, I found it quick.
Hope that helps!

Hi, Albertrahul!
Can you explane, why you devide 200 by 2?

The fact is that I've used the same approach in my solution. But I was confused with the last operation (when you devide 200 by 2). Don't you think that the first and the second terms in the set might be 90 and 110, respectively? In this case, the least number would be 90...
According to the right aswer, I am wrong... I just can't understand why

After re-reading the question I think the answer is because we want to know the maximum possible length of the shortest piece of wood.

After re-reading the question I think the answer is because we want to know the maximum possible length of the shortest piece of wood.

Hi lion147,

You are absolutely right! Thank you
I read the question not carefully enough