Latest IBM Aptitude Question SOLUTION: find the remainder when 59^73^5! is divided by 37? find the reminder when 6^65^56 is divided by 43? find the reminder when 20!+20^23 divided by 23?

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(#M40040618) IBM Numerical Ability question Keep an EYE

find the remainder when 59^73^5! is divided by 37?
find the reminder when 6^65^56 is divided by 43?
find the reminder when 20!+20^23 divided by 23?

Asked In IBM vinit (9 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

sindhu  (9 years ago)

59^73^5! / 37 => 5! = 120 (divisible by 4) => 59^73^1 / 37
73 when divided by 4 gives remainder 1.
=> 59^1/37
=> remainder is 22

Is this solution Helpfull? Yes (6) | No (1)  

radhika  (9 years ago)

can any one please explian the above 3 answers...

Is this solution Helpfull? Yes (2) | No   

divya tikki  (9 years ago)

Any number raised to the power 36 would give remainder as 1 when divied by 37.....so find the remainder of 73^5!=73^120 with respect to 36...it gives a rainder of 1...and 59 gives remainder 22 when divided by 37.....So solving it u get remainder as 22

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

Abhishek Basu  (9 years ago)

3) we know that (p-2)!/p remainder 1, when p is prime and greater than 5
hence (23-2)!/23 remainder 1
ie 21!/23 remainder 1
now we can write 21! as 21x20!
so,
21x20!/23 remainder 1
ie, 21/23 x 20!/23 remainder 1
now, for, 21/23 remainder 21 or -2
now see that if a is he remainder for 20!/23, then a x -2 should be 24 for total remainder o be 1.. (as for 24/23 remainder 1) so a =-12
so 20!/23 remainder is -12 or11

now the second part..
20^23/23
for 20/23 remainder is 20 or -3, hence remainder -3^23
for each -3^3/23 yields a remainder -4 (-27/23)
we can write -3^23/23 as (-3^3)^7 x -3^2
ie, -4^7 x-3^2/23
now each -4^3/23 yields a remainder of -5,
so for -4^7/23 yields a remainder -5^2 x -4
and -4^7 x -3^2/23 yields a remainder -5^2x-4x-3^2 ie 25x-4x9 ie 100
again 100/23 yeilds a remainder 8

previously from 1st part we got a remainder 11, and 2nd part 8..
hence total remainder 19

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

aman  (9 years ago)

59^73^5! Div by 37 reminder is 12
6^65^56 div by 43 reminder is 6
20!+20^23 reminder is 0

Is this solution Helpfull? Yes | No (9)  

dhanikar  (9 years ago)

can u please explain the answer

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