When 242 is divided by a certain divisor the remainder is 8

None of these

Musicat 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. 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

OA: C

Plugging in the answers is the quickest approach here, where we start testing from the middle option, (C) 13 in this case. See what is remainder, when 242 is divided by 13; it’s 8, oho! And also see what is remainder when 698 is divided by 13; it is 9, I love it! Now one final test, see what is the remainder when 242 + 698 = 940 is divided by 13; it is 4, now I can’t ask for more and it’s…

[spoiler](C) 13[/spoiler]

Another approach:

(1) 242 = D*N1 + 8

(2) 698 = D*N2 + 9

(3) 242+698=D*N3 + 4

Add (1) and (2) > 698+242 = D*(N1+N2) + 17

Subtract from (3) > D*(N3-N1-N2) = 13

Therefore D, the divisor, is a multiple of 13