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# A number when successively divided by 3,5 and 8 leaves remai

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Manager
Joined: 23 May 2013
Posts: 107
A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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26 Sep 2013, 06:44
5
16
00:00

Difficulty:

95% (hard)

Question Stats:

48% (02:28) correct 52% (02:41) wrong based on 226 sessions

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A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders when the order of the divisors is reversed.

A. 8,5,3
B. 4,2,1
C. 3,2,1
D. 6,4,2
E. None of above

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Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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30 Sep 2013, 19:52
6
2
ankur1901 wrote:
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders when the order of the divisors is reversed.

A. 8,5,3
B. 4,2,1
C. 3,2,1
D. 6,4,2
E. None of above

Another method is finding the first such number. You performed 3 steps:
- divide by 3, rem 1, Quotient Q
- then divide Q by 5, rem 4, Quotient Q*
- then divide Q* by 8, rem 7, Quotient Q**

Let's say the quotient (Q**) you obtained when you divided by 8 was 0. So quotient (Q*) you obtained when you divided by 5 must be 7 (to get 7 as remainder). So the number before division (Q) by 5 must be 5*7 + 4 = 39. This must be the quotient (Q) after division by 3. Original number must be 39*3 + 1 = 118

When you divide 118 by 8, remainder is 6, quotient is 14
When you divide 14 by 5, remainder is 4, quotient is 2
When you divide 2 by 3, remainder is 2

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Intern
Joined: 14 Aug 2013
Posts: 34
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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26 Sep 2013, 09:10
17
7
ankur1901 wrote:
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders when the order of the divisors is reversed.

A. 8,5,3
B. 4,2,1
C. 3,2,1
D. 6,4,2
E. None of above

A number when successively divided by 3,5,8 leaving remainders 1,4,7 can be written as 3(5(8k+7)+4)+1

=>120k+118

when this number is dived by 8 i.e (120k+118)/8=15k+14 remainder 6
(15k+14)/5=3k+2 remainder 4
(3k+2)/3=k remainder 2
And D) 6,4,2
Hope its clear
##### General Discussion
Intern
Joined: 05 Aug 2013
Posts: 2
Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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30 Sep 2013, 11:15
2
2
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders when the order of the divisors is reversed.

A. 8,5,3
B. 4,2,1
C. 3,2,1
D. 6,4,2
E. None of above

My approach would be

Three Divisors: 3, 5, 8
Three Remain: 1, 4, 7

Start from the bottom of the last column i.e. from the third remainder:

Go up diagonally and multiply by the second divisor: 5*7 = 35

Go down and add the second remainder: 35 + 4 = 39

Go up diagonally and multiply by the first divisor: 39* 3 = 117

Go down and add the first remainder: 117 + 1 = 118

Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2

Ans is D i.e. 6,4,2
Manager
Joined: 30 Mar 2013
Posts: 109
A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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05 Oct 2014, 10:15
thanks for the question. What's the source?
Manager
Joined: 30 Mar 2013
Posts: 109
Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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10 Oct 2014, 02:11
kusena wrote:
ankur1901 wrote:
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders when the order of the divisors is reversed.

A. 8,5,3
B. 4,2,1
C. 3,2,1
D. 6,4,2
E. None of above

A number when successively divided by 3,5,8 leaving remainders 1,4,7 can be written as 3(5(8k+7)+4)+1

=>120k+118

when this number is dived by 8 i.e (120k+118)/8=15k+14 remainder 6
(15k+14)/5=3k+2 remainder 4
(3k+2)/3=k remainder 2
And D) 6,4,2
Hope its clear

Hello, I don't get the red part. Why isn't the number written as 15K + remainder? That's the way we wrote it in the first portion (from which we got 120k+118)
Thanks
Intern
Joined: 28 Mar 2014
Posts: 11
Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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02 Nov 2014, 11:48
usre123 wrote:
kusena wrote:
ankur1901 wrote:
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders when the order of the divisors is reversed.

A. 8,5,3
B. 4,2,1
C. 3,2,1
D. 6,4,2
E. None of above

A number when successively divided by 3,5,8 leaving remainders 1,4,7 can be written as 3(5(8k+7)+4)+1

=>120k+118

when this number is dived by 8 i.e (120k+118)/8=15k+14 remainder 6
(15k+14)/5=3k+2 remainder 4
(3k+2)/3=k remainder 2
And D) 6,4,2
Hope its clear

Hello, I don't get the red part. Why isn't the number written as 15K + remainder? That's the way we wrote it in the first portion (from which we got 120k+118)
Thanks

Since 15/5=3 and 14/5=2 and gives 4 as remainder. Hence it is 3k+2 remainder 4

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Manager
Joined: 30 Mar 2013
Posts: 109
Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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03 Nov 2014, 00:41
it was silly question. Got it, thanks:-)
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Re: A number when successively divided by 3,5 and 8 leaves remai  [#permalink]

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23 Jan 2016, 22:05
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Re: A number when successively divided by 3,5 and 8 leaves remai &nbs [#permalink] 23 Jan 2016, 22:05
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