The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of these integers is 36 and median of these 5 integers is 28. What is the greatest possible value of Z? a) 128 b) 130 c) 140 d) 132 e) 120 Please assist with above problem.

alanforde800Maximus wrote:The integers v, w, x, y and z are such that 0 < v < w < x < y < z. The average of these integers is 36 and median of these 5 integers is 28. What is the greatest possible value of Z? a) 128 b) 130 c) 140 d) 132 e) 120 The average of these integers is 36 So, (v + w + x + y + z)/5 = 36 So, v + w + x + y + z = 180 The median of these 5 integers is 28 Since x is the middlemost value (in ascending order), we know that x = 28 So, we have v, w, 28, y, z If we want to MAXIMIZE the value of z, we must MINIMIZE the remaining values. Since v is a positive integer, the smallest value of v is 1 1, w, 28, y, z Since v < w, the smallest value of w is 2 1, 2, 28, y, z Since x < y, the smallest value of y is 29 1, 2, 28, 29, z Since v + w + x + y + z = 180, we know that 1 + 2 + 28 + 29 + z = 180 Simplify: 60 + z = 180 z = 120 Answer: E RELATED VIDEO - Mean, median and mode: https://www.gmatprepnow.com/module/gmat ... /video/800

The GMAT loves its min-max problems. For another good one, see here: https://www.beatthegmat.com/gmat-prep-av ... 75647.html

Let's make it easy on ourselves. x is the middle number of the five, so x = median = 28. The sum of the five numbers = (Average * # of #'s) = 5*36 = 180. We'll make v, w, and y as small as possible: v = 1 (it has to be greater than 0, but we want it to be as close to 0 as possible) w = 2 (it has to be greater than v, which is 1, but we want it to be as close to 1 as possible) y = 29 (it has to be greater than x, which is 28, but we want it to be as close to 28 as possible) From there, we've got Sum = v + w + x + y + z 180 = 1 + 2 + 28 + 29 + z and we're left with the max of z, or z = 120.

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