![]() Next, \(x_4\) and \(x_5\) cannot be less than the median, which is 140. We want to maximize \(x_1\), not to minimize. Why couldn't x4 and x5 be bigger than 140 and thus making x1 and x2 even smaller? Given: 5 peices of wood have an average length of 124 inches -> total length = 124*5=620. What is the MAX possible length of the shortest piece of wood? Hope it helps.ĥ peices of wood have an average length of 124 inches and a median of 140 inches. The minimum possible values of L4 and L5 could be 140, hence the L1 L2 = 620 - 420 = 200.īelow is step by step analysis of this question. they should be 100.Īpologies blink005, if I am getting this wrong. To make the smallest number as great as possible, both the small numbers should be 24 each less than the mean i.e. So the two smallest numbers should be a total of 48 less than mean, 124. Since the mean is 124, the 3 greatest numbers are already 16 each more than 124 i.e. The two greatest numbers should both be at least 140 (since 140 is the median) ![]() Using the same logic, lets make the greatest number as small as possible. If this doesn't make sense, think of a set with mean 20:ġ9, 20, 21 (smallest number very close to mean, greatest very close to mean too)ġ0, 20, 30 (smallest number far away, greatest far away too) Which means the greatest number should be as close to the mean as possible too. Basically, it should be as close to the mean as possible. The mean is given and I need to maximize the smallest number. Follow my train of thought here (which finally takes just a few seconds when you start doing it on your own)įirst thing that comes to mind - Median is the 3rd term out of 5 so the lengths arranged must look like: fun to work out, can be reasoned out fairly quickly but needs you to think a little. It is a nice question, a GMAT type question i.e. what is the maximum possible length in cm of the shortest piece of wood? ![]() Min length of the second largest piece of wood, \(x_2\) could be equal to \(x_1\) and the min lengths of \(x_4\) and \(x_5\) could be equal to 140 -> \(x_1 x_1 140 140 140=620\) -> \(x_1=100\).ĥ pieces of wood have an average length of 124 cm and a median of 140 cm. To minimize one quantity, maximize the others. To maximize one quantity, minimize the others Question: what is the MAX possible length of the shortest piece of wood? Or \(max(x_1)=?\) So if we consider the pieces in ascending order of their lengths we would have \(x_1 x_2 140 x_4 x_5=620\). If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.Īs we have odd # of pieces then 3rd largest piece \(x_3=median=140\). If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order Given: 5 peices of wood have an average length of 124 centimeters -> total length = 124*5=620. What is the maximum possible length, in centimeters, of the shortest piece of wood? Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters.
0 Comments
Leave a Reply. |