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

Question

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

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

blueseas · Accepted Answer

let that divisor be x 
since remainder is 8 or 9 it means divisor is greater than 9.
now 242-8=234 =kx (k is an integer and 234 is divisble by x)
similarly 698-9=689 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (234+689)+8+9
=x(k+l) + 17
when we divide this number by x then remainder will be equal to remainder of (17 divided by x) = 4 hence x = 17-4 = 13
hence C

Bunuel · Answer

When 242 is divided by a certain divisor the remainder obtained is 8 -->  242=q_1*d+8 
When 698 is divided by the same divisor the remainder obtained is 9 -->  698=q_2*d+9

When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4 -->  242+698=d(q_1+q_2)+17

Now, the first term ( d(q_1+q_2) ) is divisible by d, so 17 divided by d yields the remainder of 4, which is true for option C, so if d=13.

Answer: C.

twobagels · Answer

242 = a*y + 8
698 = b*y + 9

then sum of previous two is given with remainder as 4

936 = y*(a+b) + 17 -> 936 = y*(a+b) + 4
dropped by 13, so I'm assuming we are counting divisions by 13
Ans. C

Abhishek009 · Answer

(A) 11 completely dividies 242 - Reject the option.
(B) 242 leaves reminder of 8 when 11, but it leaves remainder of 1 when divided by 17 - Reject the option.
(C) 242 leaves reminder of 8 when 13, but it leaves remainder of 9 when divided by 13 , further 242 + 698 = 940, it leaves remainder of 4 when divided by 13, this is our Answer

For formality sake , check the other answers to confirm, final answer must be (C)

infowarf · Answer

y = kx + b where y is the number, x is the divisor, b is the remainder and k is the multiplier.

242 = ab + 8

698 = ad + 9

their sum will be

940 = ac + 4
940 = ab + 8 + ad + 9
ac + 4 = ab + 8 + ad + 9
ac - ab - ad = 13

As 13 is a prime number this means that c - b - d = 1, there are no multipliers, and we can state that the divisor is 13.

SergejK · Answer

Great approach, taught me again something about how to handle reminder problems. But couldn't we create 3 equations and then just look at the answer choices or am I missing an important process step? 
234=xf
689=xm
936=xz

We just start with the smallest number 234 and prime factorize it. We see that at max, there is a factor of 13. As all the other answer choces are also primes, we just check if 13 divides 689 and 936, as choice E would still be possible. Would appreciate a short feedback if my understanding is correct.

bumpbot · Answer

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

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

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