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

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Intern
Joined: 30 Jun 2012
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A number when divided by a certain divisor left remainder 24 [#permalink]

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01 Dec 2012, 08:51
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74% (02:22) correct 26% (02:44) wrong based on 283 sessions

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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?

A. 370
B. 365
C. 380
D. 456
E. 460
[Reveal] Spoiler: OA
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Joined: 22 Dec 2011
Posts: 295
Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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01 Dec 2012, 09:12
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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

Only option A gives us that.... so A it is...
Director
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Posts: 893
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
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WE: Information Technology (Investment Banking)
Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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08 Aug 2013, 23:24
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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]

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09 Aug 2013, 13:52
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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
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Asif vai.....

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Joined: 05 Jun 2011
Posts: 15
Schools: Kellog, Stern, Stanford, Booth,HBS, Wharton
Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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12 Aug 2013, 17:48
'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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Joined: 29 Mar 2013
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Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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13 Aug 2013, 11:37
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(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
Manager
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GMAT 1: 670 Q48 V34
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Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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06 Aug 2014, 04:54
Is this a sub-600 level question?
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Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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06 Aug 2014, 21:28
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

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]

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06 Aug 2014, 21:30
alphonsa wrote:
Is this a sub-600 level question?

Yes... seems to be.

There is no much calculation in this question
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Director
Joined: 23 Jan 2013
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A number when divided by a certain divisor left remainder 24 [#permalink]

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09 Oct 2015, 23:14
algebraic one;

n=qx+241, where x is divisor
2n=2(qx+241)
2n=sx+112
2qx+482=sx+112
370=sx-2qx => x(s-2q)=370.

Only option A says that x=370, so s-2q=1. We know that quotients are always integers, as well as their products and difference

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

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18 Apr 2016, 01:26
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
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Re: A number when divided by a certain divisor left remainder 24 [#permalink]

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15 May 2016, 11:15
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
Re: A number when divided by a certain divisor left remainder 24   [#permalink] 15 May 2016, 11:15
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