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Intern  Joined: 30 Jun 2012
Posts: 11
A number when divided by a certain divisor left remainder 24  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (02:08) correct 28% (02:43) wrong based on 372 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
Manager  Joined: 22 Dec 2011
Posts: 211
Re: A number when divided by a certain divisor left remainder 24  [#permalink]

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

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1
1
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 !
Senior Manager  Joined: 10 Jul 2013
Posts: 289
Re: A number when divided by a certain divisor left remainder 24  [#permalink]

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

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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... Intern  Joined: 29 Mar 2013
Posts: 24
Schools: ISB '16
Re: A number when divided by a certain divisor left remainder 24  [#permalink]

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1
(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]

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Is this a sub-600 level question? SVP  Status: The Best Or Nothing
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Re: A number when divided by a certain divisor left remainder 24  [#permalink]

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3
2
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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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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A number when divided by a certain divisor left remainder 24  [#permalink]

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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  Joined: 09 Jun 2015
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A number when divided by a certain divisor left remainder 24  [#permalink]

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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

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

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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

We can let the number = n and the divisor = d.

Since the remainder is 214 when n is divided by d, we can say:

n/d = q + 241/d

Multiplying both sides by d, we have:

n = qd + 241 [Eq. 1]

Also, since the remainder is 112 when twice n is divided by d, we can say:

2n/d = p + 112/d

Multiplying both sides by d, we have:

2n = pd + 112 [Eq. 2]

Multiplying Eq. 1 by 2, we have:

2n = 2qd + 482

Substituting 2n into Eq. 2 as 2qd + 482, we can say:

2qd + 482 = pd + 112

370 = pd - 2qd

d(p - 2q) = 370

Since (p - 2q) is an integer, d must be a factor of 370. The only number in the answer choices that is a factor of 370 is 370 itself. Thus, answer choice A is correct.

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

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_________________ Re: A number when divided by a certain divisor left remainder 24   [#permalink] 22 Jan 2019, 15:15
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