What is the remainder when the three-digit integer n is divided by 9?

Question

What is the remainder when the three-digit integer  n  is divided by 9?
1) The sum of the digits of  n  is equal to 13
2) The product of the digits of  n  is equal to 35

chetan2u · Accepted Answer

Remainder when a number, n, is divided by 9 is same as the sum of digits of that number, n, is divided by 9.

1) The sum of the digits of  n  is equal to 13
As 13 leaves a remainder of 4 when divided by 9, the number n too will leave a remainder of 4.
For example : 904= 900+ 4  and 319=315+ 4 
Sufficient

2) The product of the digits of  n  is equal to 35
Let n be xyz, so the product is x*y*z, which is equal to 35.
x*y*z=35=5*7=1*5*7
So the number can be any of 157, 175, 751, 571, 517 and 715.
Whatever be the number, the sum of digits = x+y+z=1+5+7=13, and when 13 is divided by 9, the remainder is 4.
Sufficient

D

KANNUPRIYA17 · Answer

B 
As 35=7*5 or 5*7 
So number will be either 75 or 57, in either way Remainder is 3.

nsdl1985 · Answer

Is it E?

For option A we have infinite possibilities as to how the sum will be 13 of any 3 digits. Not sufficient for deciding the remainder.

Its a 3 digit integer.

35= 1*5*7
1, 5 and 7 can be placed any how. We don't know the sequence- how they are placed. There will be 6 possibilities for the sequences 157,175, 257,275, 751,715. The remainders are different.

Not sure if my thought process is correct.

TarunKumar1234 · Answer

What is the remainder when the three-digit integer n is divided by 9?
Stat1: The sum of the digits of n is equal to 13
then we will have remainder = 4. Sufficient

Stat2: The product of the digits of n is equal to 35
then we have, digits = 1, 7 and 5, Now sum = 13, we can get the remainder, if n is divided by 9. Sufficient

So, I think D.

nsdl1985 · Answer

This was of great help. Thank you.

ravigupta2912 · Answer

I don't understand the logic for statement 1. I get the summand concept but here the sum is of the digits and not of a number that when combined with a multiple of 9 would sum upto 9. Where does the concept - if sum of digits leaves a certain remainder when divided by a number, then the number itself would also leave that very remainder - come from?

chetan2u · Answer

It is hidden in the very property of divisibility by 9.

Say 123. It adds up to 6, so remainder will be 6 when divided by 9. 
Because if you add 3 to 123 in any of digits, the number will be divisible by 9.
So 126 or 154 or 423 or 1233 all will be divisible by 9. 
123+3=126, sum =1+2+6=9.

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What is the remainder when the three-digit integer n is divided by 9?

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What is the remainder when the three-digit integer n is divided by 9?

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