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## remainder

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jainrahul1985 Really wants to Beat The GMAT!
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remainder Sat Jan 14, 2012 9:52 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
What is the remainder when 7 is divided by 10^548 ?
A. 1 B. 3 C. 6 D. 7 E. 9
OA A

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rijul007 GMAT Destroyer!
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Sat Jan 14, 2012 10:40 am
are you sure the ques is correct??

I am getting 2 as the ans...

ronnie1985 GMAT Destroyer!
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Sat Jan 14, 2012 11:44 am
Please read the question carefully. It asks what is the remainder when [b][u]7 is divided by 10^something, which is greater than 7 and hence remainder will be 7 only (D). If the question had been what's the remainder when 10^548 is divide by 7 then
Consider R(x/y) = z means remainder when x is divided by y is equal to z
R(10^548/7)=R(3^548/7)=R(9^274/7)=R(8^91x2/7)=R(1x2/7)=R(2/7)=2
Hence 2 is the remainder in that case which is not given in the options.

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ArunangsuSahu GMAT Destroyer!
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Sat Jan 14, 2012 12:09 pm
(D)

if 10^548/7 then 2

gmatpup Rising GMAT Star
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Tue Jan 17, 2012 10:00 am
Normally when I am faced with a remainder question I break the larger number down into its primes.. In this case it would be 137 (because I break down the 548) so I am getting a remainder of 0.05

guha.santanu@gmail.com Rising GMAT Star
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Tue Jan 17, 2012 6:53 pm
ronnie1985 wrote:
Please read the question carefully. It asks what is the remainder when [b][u]7 is divided by 10^something, which is greater than 7 and hence remainder will be 7 only (D). If the question had been what's the remainder when 10^548 is divide by 7 then
Consider R(x/y) = z means remainder when x is divided by y is equal to z
R(10^548/7)=R(3^548/7)=R(9^274/7)=R(8^91x2/7)=R(1x2/7)=R(2/7)=2
Hence 2 is the remainder in that case which is not given in the options.
Could you please explain how you have derived R(9^274/7)=R(8^91x2/7)=R(1x2/7)?

ronnie1985 GMAT Destroyer!
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Wed Jan 18, 2012 1:17 am
guha.santanu@gmail.com wrote:
ronnie1985 wrote:
Please read the question carefully. It asks what is the remainder when [b][u]7 is divided by 10^something, which is greater than 7 and hence remainder will be 7 only (D). If the question had been what's the remainder when 10^548 is divide by 7 then
Consider R(x/y) = z means remainder when x is divided by y is equal to z
R(10^548/7)=R(3^548/7)=R(9^274/7)=R(8^91x2/7)=R(1x2/7)=R(2/7)=2
Hence 2 is the remainder in that case which is not given in the options.
Could you please explain how you have derived R(9^274/7)=R(8^91x2/7)=R(1x2/7)?
3^548 = (3^2*274) = 9^274

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ronnie1985 GMAT Destroyer!
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Wed Jan 18, 2012 1:24 am
ronnie1985 wrote:
guha.santanu@gmail.com wrote:
ronnie1985 wrote:
Please read the question carefully. It asks what is the remainder when [b][u]7 is divided by 10^something, which is greater than 7 and hence remainder will be 7 only (D). If the question had been what's the remainder when 10^548 is divide by 7 then
Consider R(x/y) = z means remainder when x is divided by y is equal to z
R(10^548/7)=R(3^548/7)=R(9^274/7)=R(8^91x2/7)=R(1x2/7)=R(2/7)=2
Hence 2 is the remainder in that case which is not given in the options.
Could you please explain how you have derived R(9^274/7)=R(8^91x2/7)=R(1x2/7)?
3^548 = (3^2*274) = 9^274
Also when 9 is divided by 7 remainder is 2
so R(9^274/7) = R(2^274/7)
Please note that 2^273 = 2^3*91=8^91
2^274 = (8^91)*2
therefore, R(2^274/7) = R(((8^91)*2)/7)
Also note 8 divided by 7 leaves 1 as remainder.
Therefore remainder R(((8^91)*2)/7) = R(1*2/7) = 2

I hope now it is easy to undersdtand

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guha.santanu@gmail.com Rising GMAT Star
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Wed Jan 18, 2012 2:44 am
Initially I didn't understand the part "Also when 9 is divided by 7 remainder is 2 so R(9^274/7) = R(2^274/7) "
Thanks mate!

abby17 Just gettin' started!
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Fri Jan 20, 2012 11:19 pm
I assume the question is 10^548/7

Since 7 and 10 are co-prime, divide the given power (548) by 6(one less than the divisor). This division gives 2 as the remainder.
So the question now reduces to what is the remainder when 10^2 is divided by 7.
Now this is very easy to solve. 100/7 gives 2 as the remainder.

Hope this helps.

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