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

Question

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

kusena · Accepted Answer

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

KarishmaB · Answer

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

Answer (D)

khushi02 · Answer

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

usre123 · Answer

thanks for the question. What's the source?

usre123 · Answer

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

mac07 · Answer

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

Posted from my mobile device

usre123 · Answer

it was silly question. Got it, thanks:-)

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

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