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When a natural number N is successively divided by 5,6,7,8 the .......

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When a natural number N is successively divided by 5,6,7,8 the .......  [#permalink]

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New post 14 Aug 2015, 03:13
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Difficulty:

  95% (hard)

Question Stats:

39% (03:11) correct 61% (02:42) wrong based on 108 sessions

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When a natural number N is successively divided by 5,6,7,8 the remainders are 1,2,4,5. What will be the sum of the remainders if the order of the division is reversed?

A: 16
B: 14
C: 12
D: 11
E: 9
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Re: When a natural number N is successively divided by 5,6,7,8 the .......  [#permalink]

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New post 14 Aug 2015, 04:52
4
Subanta wrote:
When a natural number N is successively divided by 5,6,7,8 the remainders are 1,2,4,5. What will be the sum of the remainders if the order of the division is reversed?

A: 16
B: 14
C: 12
D: 11
E: 9


Good question.

By successive it means that we divide N first by 5 and obtain a quotient 'a' and remainder of 1. Now we divide 'a' by 6 and obtain a quotient of b and remainder of 2. Similarly, dividing 'b' by 7 gives us a quotient 'c' and remainder of 4. Finally, dividing 'c' by 8 gives us a quotient of 'd' and remainder of 5.

For any number N when divided by another number S, we get a quotient Q and remainder R such that, N = QS+R, R<N

Thus, based on the above definition of "successive division" we get,

N = 5a+1, where a = 6b+2, b = 7c+4 and c = 8d+5. Subsitituting these values back into the main equation we get,

N = 1680*d+1181

Pick any value for N now = 1181 (to simplify the calculations).

We get a remainder of 5 and quotient of 147 when divided by 8, remainder of 0 and quotient of 21 when divided by 7 , remainder of 3 and quotient of 3 when divided by 6 and remainder of 3 and quotient of 0 when divided by 5.

Thus, the sum of all the remainders = 5+0+3+3 = 11. D is the correct answer.
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Re: When a natural number N is successively divided by 5,6,7,8 the .......  [#permalink]

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New post 15 Aug 2015, 04:57
3
1
Subanta wrote:
When a natural number N is successively divided by 5,6,7,8 the remainders are 1,2,4,5. What will be the sum of the remainders if the order of the division is reversed?

A: 16
B: 14
C: 12
D: 11
E: 9

5 6 7 8
1 2 4 5

leave the top right- most number 8
start with bottom right-most number 5
5*7+4=39
39*6+2=236
236*5+1=1181
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 11
Hence, the correct option is D
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Re: When a natural number N is successively divided by 5,6,7,8 the .......  [#permalink]

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New post 23 Sep 2018, 04:31
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Re: When a natural number N is successively divided by 5,6,7,8 the .......  [#permalink]

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New post 23 Sep 2018, 04:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: When a natural number N is successively divided by 5,6,7,8 the ....... &nbs [#permalink] 23 Sep 2018, 04:31
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