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A number when divided by a certain divisor left remainder 24
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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? A. 370 B. 365 C. 380 D. 456 E. 460
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Re: A number when divided by a certain divisor left remainder 24
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01 Dec 2012, 08:12
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
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08 Aug 2013, 22:24
Easy solution:
N= Dq1+241 2N = 2Dq1 + 482  (1)
2N = Dq2 + 112  (2)
As (1) = (2) = 2N
D*(q22q1) = 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
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09 Aug 2013, 12:52
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
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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...241112=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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Re: A number when divided by a certain divisor left remainder 24
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13 Aug 2013, 10:37
(n241)/a=1 ...... 1 => n241=a (2n112)/a=1.....2 => 2n112=a
replacing a.... > 2n112=n241 =>n=129 241+129=370....uff



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Re: A number when divided by a certain divisor left remainder 24
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06 Aug 2014, 03:54
Is this a sub600 level question?



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Re: A number when divided by a certain divisor left remainder 24
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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 ExplanationAs 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
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06 Aug 2014, 20:30
alphonsa wrote: Is this a sub600 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
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09 Oct 2015, 22:14
algebraic one;
n=qx+241, where x is divisor 2n=2(qx+241) 2n=sx+112 2qx+482=sx+112 370=sx2qx => x(s2q)=370.
Only option A says that x=370, so s2q=1. We know that quotients are always integers, as well as their products and difference
A



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A number when divided by a certain divisor left remainder 24
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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 = 482112=370



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Re: A number when divided by a certain divisor left remainder 24
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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. 482112 = 370



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Re: A number when divided by a certain divisor left remainder 24
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16 Jul 2017, 16:44
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. Answer: A
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Re: A number when divided by a certain divisor left remainder 24
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