The question is about remainders and divisors. Number Theory and Number Properties are hot favorites in GMAT.
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
The correct choice is (C) and the correct answer is 13.
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 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
leaves a remainder of 4.
If the remainder obtained is 4 when 17 is divided by d, then d has to be 13.
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This eBook covers all the topics in Number Theory related to GMAT. Concepts covered in this eBook include LCM, HCF, remainder theorem, units digits, remainders and factorials in number theory. 
This eBook has 80 Problem Solving questions and 49 Data Sufficiency questions in Number Properties and Number Theory. Concepts covered include LCM, HCF, remainder theorem in number theory, factors, factorials and numerous word problems. Detailed explanatory answers provided to each question.
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