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The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t

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The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t [#permalink] New post   26 Sep 2016, 06:51
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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..
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E
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Re: The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t [#permalink] New post   26 Sep 2016, 07:10
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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

Please assist with above problem..


Hi

The middle term,x, is 28 ..
Sum is average*5=36*5=180..
Since all are different let's take the min value of other 4 to get max z..
So let v be 1, w be 2, x is 28, and y be next higher 29..
So all 4 add u to 1+2+28+29=60..
So max value of z is 180-60=120..

Hope it helps
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Re: The integers v,w,x,y and z are such that 0 [#permalink] New post   26 Sep 2016, 07:35
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I followed the above method. Since we need to maximize one term, we will have to minimize the other terms. Sum of the integers is 180. But since median is 28, the middle term will be 28 because there are 5 terms. Now, there will be 2 terms below 28 and 2 terms above 28. We need to minimize the sum of these 4 terms. Since they are all positive, we get 1+2+28+29= 60. Hence answer is 120


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Re: The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t [#permalink] New post   26 Sep 2016, 07:45
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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

Please assist with above problem..


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: [spoiler]E[/spoiler]

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Re: The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t [#permalink] New post   17 Apr 2017, 04:38
Option E

5 integers such that: z>y>x>w>v>0. Median = 28, Mean = 36. Max Z =?

x = 28, z+y+x+w+v = 36*5 = 180. To max. z, min. rest.

Assume min. v=1, min. w = 2, min. y = 29.

Max. z = 180 - 1- 2 - 28 - 29 = 120.
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Re: The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t [#permalink] New post   20 Apr 2017, 16:48
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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


We are given that the average of v, w, x, y, and z is 36. Using the formula average = sum/number, we get:

36 = sum/5

180 = sum

We are also given that the median is 28 and need to determine the greatest value of z.

To maximize the value of a single number, we minimize the values of all the other numbers, in accordance with any constraints.

v = 1

w = 2

x = 28 = median

y = 29

Thus, v + w + x + y = 1 + 2 + 28 + 29 = 60. So, the largest possible value of z is 180 - 60 = 120.

Answer: E
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Re: The integers v,w,x,y and z are such that 0<v<w<x<y<z. The average of t [#permalink]
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