remainder

Question

What is the remainder when 7 is divided by 10^548 ? A. 1 B. 3 C. 6 D. 7 E. 9 OA A

rijul007 · Answer

are you sure the ques is correct?? I am getting 2 as the ans...

ronnie1985 · Answer

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.

ArunangsuSahu · Answer

(D) if 10^548/7 then 2

gmatpup · Answer

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 · Answer

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)?

ronnie1985 · Answer

guha.santanu@gmail.com 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

ronnie1985 · Answer

ronnie1985 wrote:guha.santanu@gmail.com 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

guha.santanu@gmail.com · Answer

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 · Answer

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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