If m and n are positive integers and r is the remained when

Question

If m and n are positive integers and r is the remained when 5(10^n) + m is divided by 3, what is the value of r?

1) n=10
2) m=1

KarishmaB · Accepted Answer

5*(10^n) + m

eg. of this expression will be
50 + m
500 + m
5000 + m 
etc

When you divide 50 or 500 or 5000 etc by 3, the remainder will always be 2 (the remainder will be the same as that obtained when you divide the sum of the digits by the numbers by 3 i.e. Sum of digits of 5000 = 5+0+0+0 = 5. When you divide 5 by 3, the remainder is 2. When you divide 5000 by 3, the remainder will be 2 only)

So the remainder when 5*(10^n) + m is divided by is dependent on the value of m.

Statement 2 tells us that m = 1. 
So when 5*(10^n) + m is divided by 3, the remainder will be 0 (Remainder when 51 or 501 or 5001 is divided by 3 will be 0).

Answer (B)

BangOn · Answer

Another method

concentrate on exp 5(10^n) + m 
when divided by 3
10^n can be written as (9+1)^n 
now whatever be the value of n (given n is positive) remainder will be always 1
so remainder of expression 5(10^n) divided by 3 will be effectively remainder of 5/3 = 2

To find the remainder of the exp. now we need to know only m

thevenus · Answer

I agree with Karishma, 
50+m
500+m
.
.
500000+m , when divided by 3 will give remainder 2 +m so, the value of r will depend upon m.

felippemed · Answer

My two cents :wink:

OC2910 · Answer

we know that 5X10^N +m gives remainder 0 when sum of digits divisible by 3 else some value 
now
statement 1 : N has some value positive but we know nothing about M so sum of digits = 5+N number of zeros+m :M unknown so insufficient
statement 2: M is 1 and N has some value positive so sum of digits = 5+N number of zeros+1=6 always therefore divisible and sufficient

B
please tell if my approach is correct

amanvermagmat · Answer

Hi '

I think your approach is correct. The answer is dependent on the value of m, not n as explained in the solution above.

akoundourakis · Answer

Can anyone solve this using the EVI approach? Equation > Variable.

pierjoejoe · Answer

(5*(10^n)+m)/3 can be write as
(5*((9+1)^n)+m)/3
5/3 + ((9+1)^n)/3 + m/3
5/3 --> r =2
((9+1)^n)/3 --> r = 1 
total remainder = 2*1 + remainder of m/3
we only need to know what is the remainder of m/3
(1) does not provide with the information needed
(2) m=1 --> remainder of 1/3 --> r = 1. thus total remainder is 2*1 + 1 = 3 --> that means the remainder is zero

If m and n are positive integers and r is the remained when

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