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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
Correct answer is option 'C'. Can you explain this answer?
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When 242 is divided by a certain divisor the remainder obtained is 8. ...
When 242 is divided by a certain divisor the remainder obtained is 8.
Let the divisor be d.
When 242 is divided by d, let the quotient be 'x'. The remainder is 8.
Therefore, 242 = xd + 8
When 242 is divided by d, let the quotient be 'x'. The remainder is 8.
Therefore, 242 = xd + 8
When 698 is divided by the same divisor the remainder obtained is 9.
Let y be the quotient when 698 is divided by d.
Then, 698 = yd + 9.
Then, 698 = yd + 9.
When the sum of the two numbers, 242 and 698, is divided by the divisor, the remainder obtained is 4.
242 + 698 = 940 = xd + yd + 8 + 9
940 = xd + yd + 17
940 = xd + yd + 17
Because xd and yd are divisible by d, the remainder when 940 is divided by d should have been 17.
However, because we know that the remainder is 4, it would be possible only when 17d17d leaves a remainder of 4.
If the remainder obtained is 4 when 17 is divided by 'd', then 'd' has to be 13.
Choice C is the correct answer.
Most Upvoted Answer
When 242 is divided by a certain divisor the remainder obtained is 8. ...
Solution:
Let's assume that the divisor is 'x'.
Given, when 242 is divided by x, the remainder obtained is 8.
So, we can write, 242 = px + 8, where p is the quotient.
Simplifying the above equation, we get px = 234 ... (1)
Similarly, when 698 is divided by x, the remainder obtained is 9.
So, we can write, 698 = qx + 9, where q is the quotient.
Simplifying the above equation, we get qx = 689 ... (2)
Now, when the sum of the two numbers 242 and 698 is divided by x, the remainder obtained is 4.
So, we can write, (242 + 698) = (px + qx) + (8 + 9) = (p + q)x + 17, where (8 + 9) is added since they are the remainders when 242 and 698 are divided by x and (p + q)x is the sum of the quotients.
Simplifying the above equation, we get (p + q)x = 923 - 17 = 906 ... (3)
Substituting the values of px from equation (1) and qx from equation (2) in equation (3), we get:
234 + 689 = (p + q)x
923 = (p + q)x
x = 923/(p + q)
Now, we need to find the value of x which is a divisor of both 242 and 698. The only possible value of x can be a factor of the difference of 698 and 242 i.e., (698 - 242) = 456.
Let's check the factors of 456 to find the value of x:
- 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
We can see that only 19 is a factor of both 234 and 689. Hence, the value of the divisor x is 19.
Therefore, the correct option is (c) 13.
Let's assume that the divisor is 'x'.
Given, when 242 is divided by x, the remainder obtained is 8.
So, we can write, 242 = px + 8, where p is the quotient.
Simplifying the above equation, we get px = 234 ... (1)
Similarly, when 698 is divided by x, the remainder obtained is 9.
So, we can write, 698 = qx + 9, where q is the quotient.
Simplifying the above equation, we get qx = 689 ... (2)
Now, when the sum of the two numbers 242 and 698 is divided by x, the remainder obtained is 4.
So, we can write, (242 + 698) = (px + qx) + (8 + 9) = (p + q)x + 17, where (8 + 9) is added since they are the remainders when 242 and 698 are divided by x and (p + q)x is the sum of the quotients.
Simplifying the above equation, we get (p + q)x = 923 - 17 = 906 ... (3)
Substituting the values of px from equation (1) and qx from equation (2) in equation (3), we get:
234 + 689 = (p + q)x
923 = (p + q)x
x = 923/(p + q)
Now, we need to find the value of x which is a divisor of both 242 and 698. The only possible value of x can be a factor of the difference of 698 and 242 i.e., (698 - 242) = 456.
Let's check the factors of 456 to find the value of x:
- 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
We can see that only 19 is a factor of both 234 and 689. Hence, the value of the divisor x is 19.
Therefore, the correct option is (c) 13.
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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)11b)17c)13d)23e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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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)11b)17c)13d)23e)None of theseCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)11b)17c)13d)23e)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)11b)17c)13d)23e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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