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 .]

i got 142 as my answer

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."