Question

Each of the integers a and b is at a distance of 6 units from 8. If a and b are distinct integers,
find their sum.
(a) 18
(b) 16
(c) 13
(d) 4​

Answer 1

Given : Each of the integers a and b is at a distance of 6 units from 8.

a and b are distinct integers,

To Find :  their sum  

(a) 18

(b) 16

(c) 13

(d) 4​

Solution:

d(A,B)   distance between points A and B

d(A,B)  = | B - A|  or  B - A  if  B ≥ A   or  A - B  if A ≥ B

integers a and b is at a distance of 6 units from 8.

| a  - 8 |  = |  b - 8 |   =  6

As  a   and  b are distinct integers

so consider that

a > 8  and b <  8

a  - 8  = 6 =>  a  = 14

8 - b = 6  =>   b = 2

a + b = 14  + 2   =  16  

Hence  their sum is 16

correct option is (b) 16

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Answer 2

Answer:

Option B is the correct answer.