Number System
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Q.

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

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Solution:
Option(C) is correct

Let the divisor be $d$. 

When 242 is divided by the divisor, let the quotient be '$x$' and we know that the remainder is 8.
Therefore, $242 = xd + 8$

Similarly, let $y$ be the quotient when 698 is divided by $d$.
Then, $698 = yd + 9$.

$242 + 698 = 940 = xd + yd + 8 + 9$
$940 = xd + yd + 17$

As $xd \text{ and } yd$ are divisible by $d$, the remainder when 940 is divided by $d$ should have been 17.

However, as the question states that the remainder is 4, it would be possible only when $\dfrac{17}{d}$ leaves a remainder of 4.

If the remainder obtained is 4 when 17 is divided by $d$, then $d$ has to be 13


(4) Comment(s)


Pranoy Shit
 ()

Here we have to find the $GCD$ of $(242-8)=234$ and $(698-9)=689$ which is $13.$



John Smith
 ()

answer to the question is correct. but the way it is solved is wrong. becuase x + y is not the quotient when 940 is divided by 13.



PRATYUSH ANAND
 ()

other than 13 other options are not completely divisible.



PRATYUSH ANAND
 ()

Let the divisor be $d$.

When 242 is divided by the divisor, let the quotient be 'x' and we know that the remainder is 8.

Therefore, $242=xd+8$ ---(i)

Similarly, let y be the quotient when 698 is divided by $d$.

Then, $698=yd+9.$

$242+698=940=xd+yd+8+9$

$940=xd+yd+17$ (ii)

Till here as shown in explanation after that,

using equation (i), we get-

$dx=234$ -(iii)

from (ii) and (iii) , we get-

$dy=689$

and as except 13 other option can't give division so answer is 13.