Any of the ten digits 0 through 9 may be used in a 6-digit code, but no digit may be used more than once. If the first two digits are 1 and 7, what is the largest possible average of all 6 digits?
a)4 b)6 c)6.5 d) 7
b)6
for largest possible average u add on highest numbers u can: next highest numbers would be 9, 8, 6, and 5
1+7+9+8+6+5=36
36/6=6
The number is something like this.
1 7 9 8 6 5
Add them together and divide by 6 to find the average.
To solve this question, we need to find the largest possible average of all 6 digits in the code, given that the first two digits are 1 and 7.
Since the digits must be unique, the remaining 4 digits can be chosen from the set {0, 2, 3, 4, 5, 6, 8, 9}.
To maximize the average, we need to choose the largest possible digits for the remaining 4 positions.
Thus, the largest digits that can be chosen are 9, 8, 6, and 5.
Adding up all 6 digits: 1 + 7 + 9 + 8 + 6 + 5 = 36.
To find the average, we divide the sum by the number of digits: 36 / 6 = 6.
Therefore, the largest possible average of all 6 digits is 6, which corresponds to option (b).
So, the correct answer is (b) 6.