One column of numbers consists of 33, 58, and 17. when the digits of the
numbers are added together, the result is 3 + 3 + 5+ 8 + 1 + 7 = 27, and when
the digits of 27 are then added together, the end result is 2 + 7 = 9. if the
same process is performed on the numbers in a second column, what can be
concluded?

a. if the end result from the second column is not 9, then the sum of
the numbers in the first column is equal to the sum of the
numbers in the second column.

b. if the end result from the second column is not 9, then the sum of
the numbers in the first column is not equal to the sum of the
numbers in the second column.

c. if the end result from the second column is also 9, then the sum of
the numbers in the first column is equal to the sum of the
numbers in the second column.

d. if the end result from the second column is also 9, then the sum of
the numbers in the first column is not equal to the sum of the
numbers in the second column.

Only (B) is correct.

Step-by-step explanation:

Let, if the numbers in 2nd column are added  , the sum is  same as the sum of numbers in the 1st column and obviously all are integers and the sum is,

   (33 + 58 +17) =108---------(1)

Now , let the  3 numbers in 2nd column are,

 1.

2.  

and

3.

So, the sum of the digits of the numbers  in the 2nd colum  are,

 ( a + b +c +d +e +f +g +h + i)  -------------(2)

Now, c +f +i =  8 or 18 (since the last digit is 8 and  0 ≤ c + f +i ≤ 27)

Now,

 sum of the numbers in 2nd column,

=

  =  -----------(3)

or = -------------(4)

or = -----------(5)

it must fall in one of above 3 forms i.e., (3) or (4) or (5)

in case (3),

(a + b + c + d + e + f + g + h + i) =  (1 +8) = 9 ---- (6)

in case (4)

(a + b + c + d + e + f + g + h + i) =  (10+8) = 18 and (1 + 8) =9 ---------(7)

in case (5)

(a + b + c + d + e + f + g + h + i) = (9 + 18) = 27 and 2 + 7 = 9 -------(8)

So, when the sum of numbers in the 2nd column is equal to the sum of numbers in the 1st column, the sum of digits of the numbers in  the 2nd column will be 9.

So, when the sum of digits of the numbers in  the 2nd column is not  9, the sum of those numbers won't be equal to the sum of numbers in the 1st column.

So, only (B) is correct.

[Note , that (C) is false. e.g. when the numbers in 2nd column is 6 , 1 and 2,  then (6 +1 +2) = 9 ≠ 108 .]

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: