Latest CDS Aptitude Question SOLUTION: What will be the remainder if 4^1000/7

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(#M40032796) CDS Numerical Ability question NUMBER SYSTEM Keep an EYE

What will be the remainder if 4^1000/7

Asked In CDS Raju (10 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

RAKESH  (10 years ago)

4^1000/7
=(4^3)^333 * 4 / 7
=(7*9+1)^333*4/7
=4/7
=> remainder = 4

Is this solution Helpfull? Yes (5) | No   

aviral bhargava  (10 years ago)

whenever we get a form like ,
(ax+1)^n/a Then , the remainder is always 1
or
(ax-1)^n/a Then , the remainder is always (a-1)
Now ,solving the question by converting the problem in above given forms,
we get ,
(((4^3)^333)*4)/7
Then we are left with ,

1*4/7,
Which will leave 4 as the remainder.
Answer=4.

Is this solution Helpfull? Yes (2) | No   

IFFAT IRAM  (10 years ago)

4^1000/7
2^2000/7
(2^1998*2^2)/7
((2^3)^666*2^2)/7
((8)^666*2^2)/7
(1^666*2^2)/7 (since remainder is 1 when 7 divides 8)
this reduces the problem to 2^2/7
hence remainder 4

Is this solution Helpfull? Yes (1) | No   

priyank anand  (10 years ago)

4^1000/7
=(7-3)^1000/7
=3^1000/7
=9^500/7
=2^500/7
=(((2^3)^166)*4)/7
=>remainder=4

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Chirag Ranjan Lahiri  (10 years ago)

4^1000/7
=(7-3)^1000/7
=3^1000/7
=9^500/7
=2^500/7
=(((2^3)^166)*4)/7
=>remainder=4

Is this solution Helpfull? Yes (1) | No (1)  

soumitra mohanty  (10 years ago)

4^10^2^2=1.73*10^23

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HARSHWARDHAN  (10 years ago)

when 4^3/7 rem=1 ,so the expression becomes ((4^3)^333)*4/7 which gives 4 as rem

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KESHAV MANDAL  (8 years ago)

(remainder of 4^even no=6 and 4^odd no =4.) here 4^1000=6, now 6/7 therefor remainder=4

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