Latest Elitmus Aptitude Question SOLUTION: find the remainder when (4.4! + 5.5! + 6.6! + .. + 19.19! )/64?

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(#M40022763) ELITMUS Numerical Ability question Quant Keep an EYE

find the remainder when (4.4! + 5.5! + 6.6! + .. + 19.19! )/64?

Asked In Elitmus Narendra Pargain (10 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

Gurpreet Singh  (10 years ago)

4.4!=5!-4!
5.5!=6!-5!
.
.
19.19!=20!-19!

=>solving this we get = 20!-4!

20! is divisible by 64 therefore remainder is 64-24=40 ans

Is this solution Helpfull? Yes (44) | No (5)  

varun bhatia  (10 years ago)

remainder for 4.4!/64=32 , 5.5!/64=24 , 6.6!/64=32 , 7.7!/64=16...rest of all is divisible by 64 so net remainder will be (32+24+32+16)/64 = 40..

so answer will be 40...

Is this solution Helpfull? Yes (15) | No (1)  

kratika jain  (10 years ago)

4*4!= rem (1/(2^6))=1 it contain 2^5 in num thus rem(15/2)=1
5*5!= rem 3 it contain 2^3 in num thus rem(75/8)=3
6*6!= rem 1 it contain 2^5 in num thus rem(27/2)=1
7*7!= rem 1 it contain 2^5 in num tus rem(7*7*3*5*3/2)=1
8*8! and above are divisible by 64
thus ans 6

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Shubhangi  (9 years ago)

Notice first that 8! is divisible by 64, as 8 = 1.2.3.4.5.6.7.8 and 2.4.8 = 64;
we write 8! | 64

By the same argument j! | 64 for all j >= 8. Thus in the sum of the question,
S = 1.1! + 2.2! + ... + 19.19!
we can disregard all terms after 7.7! as all of them will have remainder 0 when divided by 64.
Now term by term,
4.4! = 96, r = 32
5.5! = 600, r = 24
6.6! = 4320, r = 32
7.7! = 35,280, r = 16
The sum is 104 which has remainder 40
So simply 40 is the answer!!

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pawann raj chauhan  (10 years ago)

so the solution as follow this question is totaly depend upon only one thing that is 5! jus see 5!=120 6!=6*120 7!=7*6*120 here we notice that after 5! factorial we get 0 because when 0 is multiply with any no. it get 0 ...whether it is 6!,7!,8!,9!,10!,11! and so on, all have zero at the end .. so notice to question 4.4!+5.120+xx0+xx0+xx0....xx will be any no. , i did nt write because we have to focus the zero which is at the end only ...4.4!+xx0=4.4.3.2.1+xx0=96+xx0=xx6......so we get 6 at the end...is it seen??
yes you are so...xx6/64..... now jus check 4 table ( 4 8 12 16 20 24 28 32 36 40) xx6 is divisible by 64 only at the 4*4=16 (6 at the end) 4*9 =36 (6 at the end) 64 devide xx6 no at 4 times or 9 times ...at question we have only one option who has last digit is 4..so that one is answer..i didnt remember the option..hope you understand it.

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naga sarath chand  (10 years ago)

1+3+1+1=6 is the ans....

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