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On dividing a certain number by 5, 7 and 8 successively, the remainder
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20 Oct 2015, 12:52
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On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders will be:[/b] (A) 3, 3, 2 (B) 3, 4, 2 (C) 5, 4, 3 (D) 5, 5, 2 (E) 6, 4, 3
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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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20 Oct 2015, 22:55
Bunuel wrote: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders will be:[/b]
(A) 3, 3, 2 (B) 3, 4, 2 (C) 5, 4, 3 (D) 5, 5, 2 (E) 6, 4, 3 Here, the concept is of successive division i.e. the no is first divided by 5 and it leaves remainder 2 and quotient is let x, therefore we have \(number = 5x + 2\)  (1) and then the quotient x is divided by 7 and the remainder is 3 so, we have x in the form of \(x = 7y + 3\) and then the quotient y is divided by 8 and the remainder is 4 so, we have x in the form of \(y = 8z + 4\) putting this value of x and y in (1) above, we get \(number = 5(7(8z +4) + 3) +2\) \(=> number = 5(56 z +31) +2\) \(=> number = 280 z + 157\) when this number will be divided by 8, we will get remainder = 5 and quotient = 35 z + 19 when this quotient will be divided by 7, we will get remainder = 5 and quotient = 5 z + 2 when this quotient will be divided by 5, we will get remainder = 2 Answer choice DKudos, if you like the explanation




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On dividing a certain number by 5, 7 and 8 successively, the remainder
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20 Oct 2015, 21:57
The number which we divided by 8 will be quotient from division by 7 = 8x + 4 The number which we divided by 7 will be quotient from division by 5 = 7(8x+4) + 3 = 56x +31 The original number which we divided by 5 =5(56x +31) + 2 = 280x +155 +2 = 280x + 157 When this number is divided by 8 = ( 280x+ 157)/8 = 35x + 19 and a remainder of 5 On dividing by 7 , ( 35x + 19) / 7 = 5x + 2 and a remainder of 5 On Dividing by 5 , (5x+2)/5 = x and a remainder of 2 Therefore the remainders will be 5,5 and 2 Answer D
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On dividing a certain number by 5, 7 and 8 successively, the remainder
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21 Oct 2015, 04:19
Bunuel wrote: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders will be:[/b]
(A) 3, 3, 2 (B) 3, 4, 2 (C) 5, 4, 3 (D) 5, 5, 2 (E) 6, 4, 3 On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively
Third divisor = 8 Third remainder = 4 i.e. Number of this type = 8+4 = 12
Second divisor = 7 Quotient then = 12 Second remainder = 3 i.e. Number of this type = 12*7+3 = 87
First divisor = 5 Quotient then = 87 Second remainder = 2 i.e. Number of this type = 87*5+2 = 437Now, successively divide by 8, 7 and 5
837 divided by 8 leaves Quotient 54 and remainder=5
54 divided by 7 leaves Quotient 7 and remainder=5
7 divided by 5 leaves Quotient 1 and remainder=2
Successive Remainders (5, 5, 2)
Answer: option D
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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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21 Oct 2015, 17:03
Bunuel wrote: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders will be:[/b]
(A) 3, 3, 2 (B) 3, 4, 2 (C) 5, 4, 3 (D) 5, 5, 2 (E) 6, 4, 3 Cross Multiplication Formula 5 7 8 2 3 4 (4*7)+3=31 (31*5)+2 = 157 Number is 157 Successive division of 157 by 8,7 and 5 will give remainder 5,5 and 2. ANSWER IS D.



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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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22 Oct 2015, 01:39
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders will be: (A) 3, 3, 2 (B) 3, 4, 2 (C) 5, 4, 3 (D) 5, 5, 2 (E) 6, 4, 3 Let the original number be X. Then by the successive dividing we have followings : X=5A+2 A=7B+3 B=8C+4. So we have A=7*(8C+4)+3=7*8C+31, and X=5*(7*8C + 31)+2 = 5*7*8C + 157. Now by dividing X by 8, 7, 5 successively we have followings : X=8*(5*7C+19)+5 5*7C+19=7*(5C+2) + 5 5C+2=5C+2. The remainders are, therefore, 5, 5, 2. The answer is (D). OR As dividing X by 8, 7, 5, we can ignore 5*7*8C(since 5*7*8C is a common multiple of 8, 7, 5, 5*7*8C doesn’t affect the remainders ). So we can consider only 157. 157=8*19 + 5 19=7*2 + 5 2=5*0+2. The remainders are 5, 5, 2.
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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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22 Apr 2016, 20:46
this is the first time when I see such a question... my approach: X is the number X=5Q+2 5Q+2 = 7Z +3 7Z+3 = 8M + 4
so X=8M+4
where did I go wrong? I believe the question is not worded properly: is the quotient only divided or together with the reminder?



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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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20 Jun 2016, 22:55
mvictor, according to your approach you are dividing the same no. by 8,7 and 5 not successively.i.e. x=5q+2, 5q+2=7z+3=x=8m+4 for dividing successively we need to divide quotient *multiple of the previous no. as explained by mathrevolution and skywalker18.



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On dividing a certain number by 5, 7 and 8 successively, the remainder
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21 Jun 2016, 22:09
to find a number first start with division by 8 when number is divided by 8 remainder is 4, so number is = 4, which is Q quotient when number which is divided by 7 and leaver a remainder 3 would be 7*4 +3 = 31 , which quotient for the number divided by 5 when number which is divided by 5 and leaver a remainder 2 would be 5*31 +2 = 157
Now 157 / 8 remainder is 5 and Q quotient is 19 , next is 19/7 remainder is 5 D is the answer.



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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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21 Jun 2016, 22:23
For a discussion on the concept of successive division and this question, check: http://www.veritasprep.com/blog/2012/10 ... division/
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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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22 Jun 2016, 00:04
Bunuel wrote: On dividing a certain number by 5, 7 and 8 successively, the remainders obtained are 2, 3 and 4 respectively. When the order of division is reversed and the number is successively divided by 8, 7 and 5, the respective remainders will be:[/b]
(A) 3, 3, 2 (B) 3, 4, 2 (C) 5, 4, 3 (D) 5, 5, 2 (E) 6, 4, 3 In successive division, the quotient will become the next dividend. Suppose number is N Then N = 5x+2; Next dividend x. x = 7y+3; Next dividend y y = 8z+4 so N = 5* {7*(8z+4) +3} +2 = 5 * (56z+31) +2 = 280 z +157 When N is divided by 8, the quotient is: 8*(35z+19) + 5First Remainder is 5. So options A, B E are out. Quotient is 35z+19; This becomes next dividend. Divide it by 7: 7 *(5z+2) + 5 Remainder is 5. > So option C is out D is the answer.



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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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19 Jun 2018, 11:38
Bunuel what is the significance of the line "When the order of division is reversed" in the question?



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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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19 Jun 2018, 21:33
chandan1988 wrote: Bunuel what is the significance of the line "When the order of division is reversed" in the question? First we divide x by 5, 7 and 8 successively, and getting the remainders of 2, 3 and 4 respectively. Then we are dividing x by 8, 7, and 5 successively(so we are dividing by the same divisors but in reverse order), and getting the remainders of 8, 7 and 5, respectively. For more on successive dividing check Successive Division post. Hope it helps.
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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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Re: On dividing a certain number by 5, 7 and 8 successively, the remainder
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