According to the question, the divisor shud divide 242-8 = 234, 698-9= 689 & 936. Look for the number that divides all the 3 number evenly. Only option C-13 satisfies the condition.

sanju09 wrote:When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?

A. 11
B. 17
C. 13
D. 23
E. None of these

Small concept.....

If A leaves remainder R1 when divided by D and B leaves remainder R2 when divided by D, the remainder when A+B is divided by D will be R1+R2 provided R1+R2 < D. In case if R1+R2 >D, it is further divided by D and the remainder is given.

Coming to our question, the remainder must be 8+9 = 17. But since it is given as 4, it is implied that 17 > our divisor and hence it is reduced to 4. So the divisor must be 13.