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A number when divided by a certain divisor left remainder 24

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A number when divided by a certain divisor left remainder 24 [#permalink] New post 01 Dec 2012, 07:51
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Question Stats:

70% (02:22) correct 30% (02:56) wrong based on 162 sessions
A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?

A. 370
B. 365
C. 380
D. 456
E. 460
[Reveal] Spoiler: OA
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 01 Dec 2012, 08:12
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apoorvarora wrote:
A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?
A 370
B 365
C 380
D 456
E 460


let the number be N we can represent N as ....

N = Quotient * Divisor + reminder

As givenN = QD + 241
2N = 2QD + 482

Now when 482 divided by one of the answer choice we should get a remainder of 112

Only option A gives us that.... so A it is...
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 08 Aug 2013, 22:24
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Easy solution:

N= Dq1+241
2N = 2Dq1 + 482 - (1)

2N = Dq2 + 112 - (2)

As (1) = (2) = 2N

D*(q2-2q1) = 370

D * Some integer = 370

Checking all options only (A) syncs with it.

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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 09 Aug 2013, 12:52
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Jp27 wrote:
apoorvarora wrote:
A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?
A 370
B 365
C 380
D 456
E 460


let the number be N we can represent N as ....

N = Quotient * Divisor + reminder

As givenN = QD + 241
2N = 2QD + 482

Now when 482 divided by one of the answer choice we should get a remainder of 112

Only option A gives us that.... so A it is...



N = Quotient * Divisor + reminder

As given N = QD + 241
2N = 2QD + 482

Now when 482 divided by one of the answer choice we should get a remainder of 112

Only option A gives us that....
sweet solution brother
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 12 Aug 2013, 16:48
VeritasPrepKarishma's posts on remainders taught me how to think about this pretty simply...
's
N/ (some divisor)+241 = a remainder of 0 right? It must be a multiple at this point and since N^2 leaves a remainder of > 241 (112) then when N is squared there must be another "grouping" of the number when divided by our mystery divisor so...241-112=129 which is = to the additional "grouping" and if 129 is the additional "grouping" then 241 + 129 must be = to the divisor which is 370!

- My terminology may be off, but if you've checked VeritasPrepKarishma's posts on divisibility you know what I mean...:)
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 13 Aug 2013, 10:37
(n-241)/a=1 ...... 1 => n-241=a
(2n-112)/a=1.....2 => 2n-112=a

replacing a.... > 2n-112=n-241
=>n=129
241+129=370....uff
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 06 Aug 2014, 03:54
Is this a sub-600 level question? :wink:
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 06 Aug 2014, 20:28
apoorvarora wrote:
A number when divided by a certain divisor left remainder 241, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?

A. 370
B. 365
C. 380
D. 456
E. 460


One step answer:

241 * 2 - 112 = 482 - 112 = 370

Explanation

As the number doubled, double the original remainder & subtract the new one
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Re: A number when divided by a certain divisor left remainder 24 [#permalink] New post 06 Aug 2014, 20:30
alphonsa wrote:
Is this a sub-600 level question? :wink:


Yes... seems to be.

There is no much calculation in this question :)
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Re: A number when divided by a certain divisor left remainder 24   [#permalink] 06 Aug 2014, 20:30
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