Latest Others Aptitude Question SOLUTION: The remainder when 10^10 +10^100 +10^1000 +.......+10^10000000000 is divided by 7 is A)0 b)1 c)2 d)5

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(#M40018523) OTHERS question Number Systems Keep an EYE

The remainder when 10^10 +10^100 +10^1000 +.......+10^10000000000 is divided by 7 is
A)0
b)1
c)2
d)5

Asked In Others Sumit Rawal (11 years ago)

Unsolved Read Solution (1)

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Read Solution (1) :

Mohammad Akram  (9 years ago)

5
10%7=3, (10^3)%7=6 => -1
so,
10^10=(10^3)^3 * 10 mod 7=(-1)*10=4
10^100=(10^3)^33 *10 mod 7=(-1)*10=4
10^1000=(10^3)^333 *10 mod 7=(-1)*10=4
10^10000=(10^3)^3333 *10 mod 7=(-1)*10=4
....
....
....
10^10000000000=(10^3)^3333333333 *10 mod 7=(-1)*10=4
so,
(4*10)%7=5

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