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

Question

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

ENGRTOMBA2018 · Accepted Answer

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.

mathivanan · Answer

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

Mansoor50 · Answer

this threw m off.....but
assuming the last quotient to be 1, i get:
8 x 1 + 5 = 13
7 x 13 +4 = 95
6 x 95 +2 = 572
5 x 572 + 1 = 2861

now i do the reverse division and get remainders: 5, 0, 3, 3 for a total of 11

samarpan.g28 · Answer

For successive divisions, we need to calculate from the back-end.
The family of numbers which when divided by 8 gives the remainder as 5=8s+5.
Similarly, we get 56s+39, 336s+236 and 1680s+1181.
Now, 1680 is divisible by 5,6,7,8 so let us divide 1181 with 8,7,6,5 (reverse order as asked in question).
1181/8 gives rem=5 and quo=147.
147/7 gives rem=0 and quo=21.
21/6 gives rem=3 and quo=3.
3/5 gives rem=3 and quo=0.
Therefore, 5+0+3+3=11. Option (D) is correct.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards