Bunuel wrote:
Joy111 wrote:
A set of numbers contains 7 integers and has an average (arithmetic mean) value as well as a median value of 23. If the largest value is equal to 15 more than 4 times the smallest number, what is the largest possible range for the numbers in the set?
A. 33
B. 35
C. 38
D. 48
E. 75
The average of 7 numbers is 23 --> the sum of these numbers is 7*23=161;
The median of 7 numbers is 23 --> 23 is the middle term: {*, *, *, 23, *, *, *};
The largest value is equal to 15 more than 4 times the smallest number --> say the smallest number is x then the largest number would be 4x+15, so our set is {x, *, *, 23, *, *, 4x+15};
Now, in order to maximize the range we need to make the second and the third numbers equal to x and the fifth and sixth numbers equal to 23, so the set should be {x, x, x, 23, 23, 23, 4x+15}.
Since the sum is 161 then x+x+x+23+23+23+4x+15=161 --> x=11.
The range is (4x+15)-x=3x+15=48.
Answer: D.
Bunuel
hi
your solution to the problem is very brilliant as usual
I have, however, two very simple questions to your kind consideration
1.
x _ _ 23 _ _ 4x + 15
here, in order to maximize the range, we comfortably can set 2nd and 3rd numbers equal to "x", but this change will not distort the mean.
can you, please, comment something on this...?
2.
here, in this question, the test maker has kindly provided us the arithmetic mean. If there was, however, no mention of the average, and if the numbers were needed not to be distinct, can the following sequence be established as long as the largest value is equal to 15 more than 4 times the smallest number...?
23, 23, 23, 23, 24, 24, 107
range = 84
And, if the numbers were needed to be distinct, then is the following pattern legitimate...?
20, 21, 22, 23, 24, 25, 95
range = 75
maybe they are very obvious, but I am badly in need of your help
thanks in advance, man
yes, 23 is median here, so we can easily adjust numbers, but here we are also given the mean
3, 4, 6 and many more.
Look here we are free to chose any number, but when we are given the average, for example 5, we are not free to chose any number
in this line of reasoing, I asked to you how you set 2 numberes equal to "x". Obvously you are very right, but I wanted to know the science behind it
yes, now I can understand, here in this question you have provided the solution for, mean and median are the same number, so this mechanixm is permissible
in the exapmple, however, I have cited, mean and median are not the same, so only 1st one fits in