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the value of the divisor

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the value of the divisor

by sanju09 » Tue Apr 05, 2011 4:57 am
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) 13
(C) 17
(D) 19
(E) 23
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by Anurag@Gurome » Tue Apr 05, 2011 5:16 am
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) 13
(C) 17
(D) 19
(E) 23
Dividend = Quotient * Divisor + Remainder
Let the Quotient = Q1 (in 1st case) , Q2(in 2nd case), and divisor = D
Then, 242 = Q1*D + 8
698 = Q2*D + 9
242 + 698 = Q1*D + 8 + Q2*D + 9
implies 940 = Q1*D + Q2*D + 17
Now, Q1*D and Q2*D are both divisible by D, so when 940 is divided by D, the remainder should be 17. But according to the question, the remainder is 4. This means 17/D gives a remainder of 4, and this is possible if D = 13

The correct answer is B.
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