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Source: — Problem Solving |
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by rijul007 » Sat Jan 14, 2012 9:40 am
are you sure the ques is correct??

I am getting 2 as the ans...
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by ronnie1985 » Sat Jan 14, 2012 10:44 am
Please read the question carefully. It asks what is the remainder when 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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by ArunangsuSahu » Sat Jan 14, 2012 11:09 am
(D)

if 10^548/7 then 2
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by gmatpup » Tue Jan 17, 2012 9:00 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
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by [email protected] » Tue Jan 17, 2012 5:53 pm
ronnie1985 wrote:Please read the question carefully. It asks what is the remainder when 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)?
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by ronnie1985 » Wed Jan 18, 2012 12:17 am
[email protected] wrote:
ronnie1985 wrote:Please read the question carefully. It asks what is the remainder when 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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by ronnie1985 » Wed Jan 18, 2012 12:24 am
ronnie1985 wrote:
[email protected] wrote:
ronnie1985 wrote:Please read the question carefully. It asks what is the remainder when 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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by [email protected] » Wed Jan 18, 2012 1:44 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!
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by abby17 » Fri Jan 20, 2012 10:19 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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