A
B
C
D
E
Let the 4 different positive integers be A, B, C, and D such that A < B < C < Dguerrero wrote:The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?
12
14
15
16
17
OAB
Sum = number * average.guerrero wrote:The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?
12
14
15
16
17
OAB
Brent how can we assume A < B < C < DBrent@GMATPrepNow wrote:Let the 4 different positive integers be A, B, C, and D such that A < B < C < Dguerrero wrote:The average (arithmetic mean) of four distinct positive integers is 10. If the average of the smaller two of these four integers is 8, which of the following represents the maximum possible value of the largest integer?
12
14
15
16
17
OAB
The average (arithmetic mean) of four distinct positive integers is 10
So, (A+B+C+D)/4 = 10
This means A+B+C+D = 40
The average of the smaller two of these four integers is 8
So, the average of A and B is 8
In other words, (A+B)/2 = 8
So, A+B = 16
Since we already know that A+B+C+D = 40, we can replace A+B with 16 to get:
16+C+D = 40
So, C + D = 24
We want to maximize the value of D. To do this, we need to minimize the value of C.
Also, since B < C, we want to minimize the value of B.
Since A+B = 16, the smallest possible value of B is 9.
So, we get A = 7
B = 9
So, C = 10 is the smallest we can make C
This means that D = [spoiler]14[/spoiler]
Answer = B
Cheers,
Brent
We're told that the 4 integers are distinct, which means no two values are the same.faraz_jeddah wrote: Brent how can we assume A < B < C < D
The question does not tell us that they are arranged in ascending order.
The 4 numbers could be - 1 15 7 17 which would make 17 the max value.
Solution:
