Question : Two numbers, when divided by a certain divisor, leave the remainder 57. When the sum of the two numbers is divided by the same divisor, the remainder is 49. The divisor is:
Option 1: 56
Option 2: 57
Option 3: 49
Option 4: 65
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Correct Answer: 65
Solution : Let the two numbers be $a$ and $b$ and the divisor is $d$. According to the question, $a = d×p + 57$ and $b=d×q + 57$, where $p$ and $q$ are the quotients. Adding these two equations we get, $(a+b)=d(p+q)+114$ Again when the sum of the two numbers is divided by the same divisor, the remainder is 49. $\therefore$ Divisor = (114 – 49) = 65 Hence, the correct answer is 65.
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