Problem Solving

ktrout2020 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

Source: Veritas

So, we have all the positive integers with median = x = 28, the middle-most integer. Let's assign the minimum possible values for v, x and y so that we have the greatest possible value of z. Minimum value of v = 1, w = 2 and y = 29 (1 greater than x).

Thus, the sum of v, w, x, y and z = 1 + 2 + 28 + 29 + z = 36*5 => z = 120

The correct answer: E

Hope this helps!

-Jay
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ktrout2020 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

Source: Veritas

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

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ktrout2020 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

Source: Veritas

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