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

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.

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

moutar wrote: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]

I meant B. I had the write answer though.

sacx wrote: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!