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

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Difficulty:

55% (hard)

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?

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

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

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

Re: A number when divided by a certain divisor left remainder 24 [#permalink]
09 Aug 2013, 12:52

1

This post received KUDOS

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 _________________

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