Problem Solving

Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

a)60
b)80
c)100
d)120
e)140

Sorry wanted to post somewhere, answered somewhere

I am between A and C

what is the source?

vinay1983 wrote:Is the OA A

No.

OA - C

in order to do the shortest length max we have to do 4th and 5th lenght min, which could be 140
now 620-420 = 200 , so distribution 100,100,140,140,140

vinay1983 wrote:Sorry wanted to post somewhere, answered somewhere

I am between A and C

what is the source?

Source: Some random PDFs which I am solving

Even though this question is easy, but the last line is confusing.

"What is the maximum possible length, in centimeters, of the shortest piece of wood?" --> you need to find maximum smallest length..
So,
you cannot assume --> x, 140, 140, 140, 140 .. as by doing so you will get the smallest possible length; we don't need that...

Correct Assumption will be : x, x, 140,140,140 --> 100

Answer {C}

theCodeToGMAT wrote:

vinay1983 wrote:Sorry wanted to post somewhere, answered somewhere

I am between A and C

what is the source?

Source: Some random PDFs which I am solving

Even though this question is easy, but the last line is confusing.

"What is the maximum possible length, in centimeters, of the shortest piece of wood?" --> you need to find maximum smallest length..
So,
you cannot assume --> x, 140, 140, 140, 140 .. as by doing so you will get the smallest possible length; we don't need that...

Correct Assumption will be : x, x, 140,140,140 --> 100

Answer {C}

Actually yes, I found that 100 should be the correct number.Used the same method.

theCodeToGMAT wrote:Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

a)60
b)80
c)100
d)120
e)140

_ _ 140 _ _
_ _ 140 140 140
a a 140 140 140

420 + 2a = 5*124
420 + 2a = 620
2a = 200
a = 100

Choose C

Cheers

theCodeToGMAT wrote:Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of the shortest piece of wood?

a)60
b)80
c)100
d)120
e)140

Let the pieces be arranged in ascending Order of their Length as follows -

A , B , C , D , E

Or , A > B > C > D > E

Arithmetic mean length of 124.

Length of all the pieces is 124*5 = 620 cm

So A + B + C + D + E = 620

Now the part " median length of 140 centimeters " means its the value below which 50% of the cases fall.

Here 50% of the 5 pieces will be 3.

So , A > B > 140 > 140 > 140

So we have A + B + 420 = 620

Hence A + B = 200


Now it boils down to A + B is 200 and we simply require to maximize A.

Keep Checking the options -

a. A = 60 , then B = 40 [ Can be maximized further ]

b. A = 80 , then B = 20 [ Can be maximized further ]

c. A = 100 , then B = 100 Can not be maximized further

d . A = 120 , then B = 80 Not possible because here A becomes more than B and violates our condition of arrangement of the pieces as A > B > C > D > E

e. A = 140 , then B = 60 Not possible because here A becomes more than B and violates our condition of arrangement of the pieces as A > B > C > D > E


Hope this helps...

A median of 140, tells us that our lengths (in ascending order) are ?, ?, 140, ?, ?
To MAXIMIZE the length of the shortest piece, we need to MINIMIZE the lengths of the 2 longest pieces (and keep a median of 140)

So, we get ?, ?, 140, 140, 140

The two remaining numbers must add to 200 (to get a sum of 620)
The way to MAXIMIZE the shortest piece is to make both remaining lengths 100.
We get 100, 100, 140, 140, 140

Answer: B

Hi Brent ,

Everything is clear. Just a quick question.

Why can not we do like this ? 140 140 140 140

Then we will get the minimum possible length = 60

Please explain.

Many thanks in advance.

SJ