shortest piece of wood

[sanju09]

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. 90
B. 100
C. 110
D. 130
E. 140


OA B

[moutar]

Let the 5 lengths be: a, b, c, d, e (a≤b≤c≤d≤e)

c = median = 140

We need to minimise d & e to maximise a.

Minimum value of d&e = 140

Total length = 124*5 = 620

a+b=720-(3*140)=620-420= 200

Minimum value of a when a=b

Therefore, a=200/2=100. Answer D.

[sacx]

Average length of 5 pieces = 124

total length = 124 * 5 = 620

now we are given median = 140

a,b,140,c,d

to maximise the length of the shortest piece of wood c and d must equal 140

a,b,140,140,140

a+b+140+140+140 = 620
a+b = 200

to maximise the length a =b

2a = 200
a = 100

[sanju09]

Let the 5 lengths be: a, b, c, d, e (a≤b≤c≤d≤e)

c = median = 140

We need to minimise d & e to maximise a.

Minimum value of d&e = 140

Total length = 124*5 = 620

a+b=720-(3*140)=620-420= 200

Minimum value of a when a=b

Therefore, a=200/2=100. Answer D.

[spoiler]Howdy! How D? [/spoiler]

[moutar]

I meant B. I had the write answer though.

[margogan]

Average length of 5 pieces = 124

total length = 124 * 5 = 620

now we are given median = 140

a,b,140,c,d

to maximise the length of the shortest piece of wood c and d must equal 140

a,b,140,140,140

a+b+140+140+140 = 620
a+b = 200

to maximise the length a =b

2a = 200
a = 100

This is the best reply! Easy to understand, thanks!