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

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If m and n are positive integers and r is the remained when [#permalink]

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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
[Reveal] Spoiler: OA

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Re: If m and n are positive integers and r is the remained when [#permalink]

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fozzzy wrote:
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


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)
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Re: If m and n are positive integers and r is the remained when [#permalink]

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New post 19 Jan 2013, 03:09
fozzzy wrote:
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


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
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Re: If m and n are positive integers and r is the remained when [#permalink]

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New post 20 Jan 2013, 10:34
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.
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Re: If m and n are positive integers and r is the remained when [#permalink]

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My two cents :wink:
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Re: If m and n are positive integers and r is the remained when [#permalink]

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New post 02 Feb 2018, 06:52
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
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Re: If m and n are positive integers and r is the remained when [#permalink]

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StrugglingGmat2910 wrote:
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


Hi '

I think your approach is correct. The answer is dependent on the value of m, not n as explained in the solution above.
Re: If m and n are positive integers and r is the remained when   [#permalink] 02 Feb 2018, 08:26
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