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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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Verified Answer
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 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.
Choice C is the correct answer.
Most Upvoted Answer
When 242 is divided by a certain divisor the remainder obtained is 8. ...
Given Information:
242 leaves a remainder of 8 when divided by the divisor.
698 leaves a remainder of 9 when divided by the divisor.
The sum of 242 and 698 leaves a remainder of 4 when divided by the divisor.
Explanation:
Let's assume the divisor is 'x'.
When 242 is divided by 'x', the equation can be written as 242 = qx + 8 (where q is the quotient).
Similarly, when 698 is divided by 'x', the equation can be written as 698 = px + 9.
And when the sum of 242 and 698 is divided by 'x', the equation can be written as (242 + 698) = rx + 4.
Now, we can rewrite the last equation as 940 = rx + 4.
Solving the equations:
From the first equation, we can rewrite it as x = (242 - 8)/q = 234/q.
From the second equation, we can rewrite it as x = (698 - 9)/p = 689/p.
Since x is the same divisor in all cases, we can equate the two expressions for x:
234/q = 689/p
234p = 689q
p = 689q/234
Substitute the value of p in the equation 940 = rx + 4:
940 = r(689q/234) + 4
940 = (689rq + 4*234)/234
940 = (689rq + 936)/234
689rq = 234(940 - 4)
689rq = 234*936
689rq = 218784
r = 218784/(689q)
Therefore, the divisor 'x' must be a factor of 218784.
Conclusion:
After calculating the factors of 218784, we find that 13 is the divisor that satisfies all the given conditions. Hence, the correct answer is option C.
242 leaves a remainder of 8 when divided by the divisor.
698 leaves a remainder of 9 when divided by the divisor.
The sum of 242 and 698 leaves a remainder of 4 when divided by the divisor.
Explanation:
Let's assume the divisor is 'x'.
When 242 is divided by 'x', the equation can be written as 242 = qx + 8 (where q is the quotient).
Similarly, when 698 is divided by 'x', the equation can be written as 698 = px + 9.
And when the sum of 242 and 698 is divided by 'x', the equation can be written as (242 + 698) = rx + 4.
Now, we can rewrite the last equation as 940 = rx + 4.
Solving the equations:
From the first equation, we can rewrite it as x = (242 - 8)/q = 234/q.
From the second equation, we can rewrite it as x = (698 - 9)/p = 689/p.
Since x is the same divisor in all cases, we can equate the two expressions for x:
234/q = 689/p
234p = 689q
p = 689q/234
Substitute the value of p in the equation 940 = rx + 4:
940 = r(689q/234) + 4
940 = (689rq + 4*234)/234
940 = (689rq + 936)/234
689rq = 234(940 - 4)
689rq = 234*936
689rq = 218784
r = 218784/(689q)
Therefore, the divisor 'x' must be a factor of 218784.
Conclusion:
After calculating the factors of 218784, we find that 13 is the divisor that satisfies all the given conditions. Hence, the correct answer is option C.
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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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