Latest Elitmus Aptitude Question SOLUTION: what is the remainder when 4.4!*5.5!*6.6!...........19*19! is divided by 64

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(#M40154095) ELITMUS Numerical Ability question remainder Keep an EYE

what is the remainder when 4.4!*5.5!*6.6!...........19*19! is divided by 64

Asked In Elitmus Deepanshu Gupta (8 years ago)

Unsolved Read Solution (13)

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Read Solution (13) :

RAGHU  (8 years ago)

i) if the question is 4.4!*5.5!*6.6!...........19*19! then answer is zero
ii) if the question is 4*4! + 5*5! + 6*6! +...................+ 19*19! answer is 3.
in second case : from from 8*8!, it will be divisible.(bcaz futhur in 9!, there will be 8*4*2 ) and from 4*4! to 7*7!

if u take common 24 i.e 4! , 24(4+25+30+1470)/64, 3(1529)/8 , remainder will be 3.

Is this solution Helpfull? Yes (15) | No (5)  

Nihar Ranjan Mohanty  (8 years ago)

4.4!+5.5!+6.6!...........19+19!
(5-1)4!+(6-1)5!+(7-1)6!..............+(20-1)19!
5!-4!+6!-5!+7!-6!.............+20!-19!
20!-4!

(20!-4!)/64
(20!/64)-(4!/64)

(20!/64)=r(0)
(4!/64)=r(3)


anzs 3

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Rahul Navariya  (8 years ago)

I think Zero(0)
because (4*4*3*2*5*5!*6*5*.......*1*7*7!..........)/64=(int value) no remender there

Is this solution Helpfull? Yes (10) | No (7)  

arpit srivastava  (7 years ago)

All the above terms greater than or equal to 8.8! , they will be completely divisible by 64.

Now the question becomes : 4.4! + 5.5! + 6.6! + 7.7!

dividing each of the four term seperately, the remainders will be 32 , 24 , 32 , 16

So adding these remainders together will make 106 and again dividing them by 64 will gives the final remainder as : 40

Is this solution Helpfull? Yes (9) | No (1)  

shehzad  (7 years ago)

The remainder would be 40
as the final result will be (20!-4!)/64 = 20!/64 - 4!/64
20!/64 = 0
-4!/64 = -24/64
which gives -24 as remainder which means real answer would be -24+64= 40

Is this solution Helpfull? Yes (9) | No   

Sourabh Prasad  (8 years ago)

Actual question is
4*4! + 5*5! + 6*6! +...................+ 19*19! is dividede by 64.
Find the remainder.
1) 3
2) 3√3
3) 9/2
4) don't remember

Is this solution Helpfull? Yes (5) | No (4)  

SG  (8 years ago)

4.4!+5.5!+6.6!...........19+19!
(5-1)4!+(6-1)5!+(7-1)6!..............+(20-1)19!
5!-4!+6!-5!+7!-6!.............+20!-19!
20!-4!

(20!-4!)/64
(20!/64)-(4!/64)

(20!/64)=r(0)
(4!/64)=r(4)

therefore combined the remainder is 60(-4)

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nashrah  (7 years ago)

40 is the ans
since 20!/64 rem is 0
4!/64 we get 24 rem
so 20!/64-2!/64 gives rem as 0-24/64=-24/64=40/64 so 40 is the rem

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Koushlendra Mishra  (8 years ago)

zero..... cz its a multiplication chain and one can easily spot a 8*8 in the series!!

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Amit Kumar Singh  (7 years ago)

From 8! Containing 8*7*6*5*4*3*2 =64*7*6*5*3
From 8 onwards totally divisible by 64 leaving remainder as zero
Before 8! Total value = 40296/64 = 40 remainder

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saketh  (8 years ago)

56 is the answer.As after 7! every number is divisible by 64,,,add upto 7! and divide hat by 64 to get remainder

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KIRAN  (8 years ago)

ans is 20;for dividng by 64 ,we want 2 power 6,which is possible after 8*8!.so upto 4*4!+5*5!+6*6!+7*7!which when divide by 64 gives remainder 20.check .i have done it.if any mistake correct me.

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chaitalibanerjee  (8 years ago)

Bt the option r different

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