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A number when divided by a certain divisor left remainder 24 [#permalink]

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01 Dec 2012, 07:51

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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?

Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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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 given\(N = QD + 241\) \(2N = 2QD + 482\)

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

Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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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.

Rgds, TGC !
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Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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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 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.... 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
_________________

Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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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...

Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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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
_________________

A number when divided by a certain divisor left remainder 24 [#permalink]

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18 Apr 2016, 00:26

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

n=241(mod d) 2*n=482(mod d); also 2*n=112(mod d); therefore d = 482-112=370

Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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15 May 2016, 10:15

i have a simple method to solve this problem.

in 1st case , remainder is 241 and in 2nd case remainder is 112. the question says twice the first number, so if we multiply the number in the 1st case, remainder should have been 2*241 = 482, but remainder is given as 112. Since divisor is same, we can get the answer by subtracting 112 from 482 i.e. 482-112 = 370

gmatclubot

Re: A number when divided by a certain divisor left remainder 24
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15 May 2016, 10:15

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