Latest CAT Aptitude Question SOLUTION: what is the remainder when 39! is divided by 41

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(#M40010549) CAT question Keep an EYE

what is the remainder when 39! is divided by 41

Asked In CAT pankaj dhami (11 years ago)

Solved PARAG KAMRA Read Solution (5)

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vivek tiwari  (11 years ago)

ans=1
39!/41
1*2*3*4....*39/41
rem(1/41)+rem(2/41)+rem(3/41)....+rem(39/41)
=rem((1+2+3+...39)/41)
=rem(780/41)
=1

Is this solution Helpfull? Yes (9) | No (3)  

nagesh  (11 years ago)

(3!/5) has a reminder of 1
(5!/7) has a reminder of 1
(9!/11) has a reminder of 1
by observing above situation (prime no-2)!/(prime no) has a reminder of 1

so i'm thinking that ans is 1

Is this solution Helpfull? Yes (8) | No (1)  

PARAG KAMRA  (11 years ago)

by wilson's theorm,we can 40!+1 is divisible by 41
so remainder 40!/41=41-1=40
so we can say that remainderwhen 40! is divide by 41 is 40
so we written as
40!=41k+40
40*39!=41k+40,the R.H.S give remainder 40 with 41,therefore
L.H.S also give 40 remainder with 41
L.H.S=40*39! where 40 gives rem 40 with 41
terefore 39! should give remainder 1 with 41

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SDeep Bhattacharya  (11 years ago)

@ PRAG KAMRA:

How can u say that :: 39! can be written as (41!-2!)..

U can say that 39!=(41-2)!

But that really doesn't mean that 39!=(41!-2!)

I can understand that u have made a silly mistake..Which all of us commit often..Just think a little bit carefully..
I'm also Thinking over the problem..

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PARAG KAMRA  (11 years ago)

39! can be written as (41!-2!)
(41!-2!)%41
so clearly 2! comes(not sure)

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