When 242 is divided by a certain divisor the remainder obtained is 11. When 698 is divided by the same divisor the remainder obtained is 18. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 9. What is the value of the divisor? Select:
A) 11  B) 17  C) 13  D) 20  E) None of these
let that divisor be x   since remainder is 11 or 18 it means divisor is greater than 18.   now  242-11= 
<gadget id="calculator"> 242-11</gadget>
<output>231</output>
231=kx (k is an integer and 234 is divisble by x)   similarly  698-18= 
<gadget id="calculator"> 698-18</gadget>
<output>680</output>
680= lx (l is an integer and 689 is divisible by x)   adding both 698 and 242   = (231+680)+11+18   =x(k+l) + 29   when we divide this number by x then remainder will be equal to remainder of (29 divided by x) = 9 hence x = 29-9= 
<gadget id="calculator">29-9</gadget>
<output>20</output>
20   hence 20
<result>D</result>
When 242 is divided by a certain divisor the remainder obtained is 11. When 698 is divided by the same divisor the remainder obtained is 18. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 9. What is the value of the divisor?