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 integers v, w, x, y and z are such that 0 < v < w
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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).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
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!
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The average of these integers is 36ktrout2020 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, (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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We are given that the average of v, w, x, y, and z is 36. Using the formula average = sum/number, we get: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
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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