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?
Choose the correct choice from the following
A) 33 B) 35 C) 38 D) 48 E) 75
The average of 7 numbers is 23 --&gt; the sum of these numbers is 7*23= 
<gadget id="calculator">7*23</gadget>
<output>161</output>
161;   The median of 7 numbers is 23 --&gt; 23 is the middle term: {*, *, *, 23, *, *, *};   The largest value is equal to 15 more than 4 times the smallest number --&gt; 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 --&gt; x=11.   The range is (4x+15)-x=3x+15=48.   Answer: 48.
<result>D</result>
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?