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When 242 is divided by a certain divisor the remainder obtai

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When 242 is divided by a certain divisor the remainder obtai  [#permalink]

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New post 22 Aug 2013, 11:05
2
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A
B
C
D
E

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Question Stats:

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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

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Re: When 242 is divided by a certain divisor the remainder obtai  [#permalink]

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New post 22 Aug 2013, 11:13
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Asifpirlo 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. 17
C. 13
D. 23
E. None of these


let that divisor be x
since remainder is 8 or 9 it means divisor is greater than 9.
now 242-8=234 =kx (k is an integer and 234 is divisble by x)
similarly 698-9=689 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (234+689)+8+9
=x(k+l) + 17
when we divide this number by x then remainder will be equal to remainder of (17 divided by x) = 4 hence x = 17-4 = 13
hence C
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Re: When 242 is divided by a certain divisor the remainder obtai  [#permalink]

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New post 22 Aug 2013, 11:14
3
1
Asifpirlo 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. 17
C. 13
D. 23
E. None of these


When 242 is divided by a certain divisor the remainder obtained is 8 --> \(242=q_1*d+8\)
When 698 is divided by the same divisor the remainder obtained is 9 --> \(698=q_2*d+9\)

When the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4 --> \(242+698=d(q_1+q_2)+17\)

Now, the first term (\(d(q_1+q_2)\)) is divisible by d, so 17 divided by d yields the remainder of 4, which is true for option C, so if d=13.

Answer: C.
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Re: When 242 is divided by a certain divisor the remainder obtai  [#permalink]

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New post 26 Nov 2018, 17:46
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Re: When 242 is divided by a certain divisor the remainder obtai &nbs [#permalink] 26 Nov 2018, 17:46
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