A number when divided by a certain divisor left remainder 24

Question

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

Jp27 · Accepted Answer

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...

PareshGmat · Answer

One step answer:

241 * 2 - 112 = 482 - 112 = 370

Explanation

As the number doubled, double the original remainder & subtract the new one

TGC · Answer

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 !

Asifpirlo · Answer

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

IvanW · Answer

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...

countonhearts · Answer

(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

alphonsa · Answer

Is this a sub-600 level question? :wink:

PareshGmat · Answer

Yes... seems to be. There is no much calculation in this question

Temurkhon · Answer

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

Mathivanan Palraj · Answer

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

brs1cob · Answer

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

ScottTargetTestPrep · Answer

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

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

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.

Answer: A

Kinshook · Answer

Given: 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. 
Asked: Find the divisor?

Let the number be X divisor be D.

X = Dk + 241; where k is an integer
2X = 2Dk + 482 = Dm + 112
2Dk + 482 = Dm + 112 
(m-2k)D = 370 = 37*2*5

Since D>241 - > D=370

IMO A

mysha · Answer

number when divided by a divisor leaves remainder 24 when twice the original number is divided by same divisor it leaves reminder 11

Bunuel · Answer

I believe that question is discussed here: https://gmatclub.com/forum/a-number-whe ... 44257.html Hope it helps.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A number when divided by a certain divisor left remainder 24

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A number when divided by a certain divisor left remainder 24

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards