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PS: Remainder Prob

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ggarr
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PS: Remainder Prob [#permalink] New post   30 Apr 2007, 15:57
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can someone solve this algebraically?

When n is divided by 7, the remainder is 5. what is the remainder when 2n is divided by 7?



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Re: PS: Remainder Prob [#permalink] New post   30 Apr 2007, 17:40
when n is divided by 7 , remainder is 5:
n = 7x + 5 where x is an integer
multiply both sides by 2
2n = 14x + 10
2n = 7(2x+1) + 3
2x+1 will always be an integer hence 3 is the remainder.

Hope it helps
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Re: PS: Remainder Prob [#permalink] New post   01 May 2007, 01:20
ggarr wrote:
can someone solve this algebraically?

When n is divided by 7, the remainder is 5. what is the remainder when 2n is divided by 7?


n=7x+5
2n=2(7x+5)=14x+10
Now 2n/7=(14x+10)/7 now 14x is divisible by 7 and hence it will yeild no remainder,while 10 will yeild a reminder 3 when divided by seven. Hence the answere is 3.

Javed.

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Re: PS: Remainder Prob [#permalink] New post   01 May 2007, 02:14
n = 7q + 5

2n = 14q + 10

2n/7 = 2q + 10/7

The 10/7 will give a remainder of 3.
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Re: PS: Remainder Prob [#permalink] New post   01 May 2007, 09:38
ggarr wrote:
can someone solve this algebraically?

When n is divided by 7, the remainder is 5. what is the remainder when 2n is divided by 7?


There are couple of wonderful Remainder questions on GMATUNI.com that you may want to check out. I just learned them this morning so this is a good practice.

Let n=number, q=quotient, d=divisor, and r=remainder.

We know that: n=q*d+r.

Here, d=7 and r=5.

n=q*7+5.

2n = 2(7q+5)
2n = 14q+10

When 2n is divided by 7....(14q+10) is divided by 7. Therefore,
2n/7 = (14q/7) + (10/7) and the remainder would be the remainder from 10/7, which is 3.



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Re: PS: Remainder Prob [#permalink]
01 May 2007, 09:38
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