Latest Elitmus Aptitude Question SOLUTION: what is the reminder when 4.4!+5.5!+6.6!+7.7!+..............+19.19! is divided by 64.

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(#M40038800) ELITMUS Numerical Ability question 31Aug Elitmus Keep an EYE

what is the reminder when 4.4!+5.5!+6.6!+7.7!+..............+19.19! is divided by 64.

Asked In Elitmus suraj Khanduri (10 years ago)

Unsolved Read Solution (10)

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Read Solution (10) :

RAKESH  (10 years ago)

E = 4*4! + 5*5! + 6*6! ........19*19!
E = (5-1)*4! + (6-1)*5! + (7-1)*6! ........(20-1)*19!
E = (5!-4!)+(6!-5!)+(7!-6!)+.........+(20!-19!)
E = (20!-4!)

E/64 = (20!-4!)/64
=> rem = 0-24/64 = -24/64
=> rem = -24+64 = 40

Is this solution Helpfull? Yes (92) | No (2)  

ankit singh parihar  (10 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!=20*19*18...16...*4*...1
as 16*4=64....the rem we get as 0
so dividing 20!/64=0(as rem is 0)
rem=0-4!/64=-24/64=64-24=40
hence ans is 40

Is this solution Helpfull? Yes (25) | No   

Vivek Pathane  (10 years ago)

can anyone explain how
(20!-4!)/64
=0-24/64
???

Is this solution Helpfull? Yes (16) | No (1)  

Mohit Mathuriya  (10 years ago)

40..8.8! is divisible by 64..we have to calculate 4.4!+5.5!+6.6!+7.7!/64 that is =40

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

ranjitkumar  (10 years ago)

40
(5-1)4!+..........(20-1)5!
(5!-4!+6!-5!........20!-19!)/64
(20!-4!)/64
(0-4!)/64
-24/64
64-24=40

Is this solution Helpfull? Yes (6) | No   

aditya saraswat  (10 years ago)

40

Is this solution Helpfull? Yes (1) | No   

niti  (10 years ago)

what is the formula to calculate the sum of factorial of n natural number?

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Swetha  (10 years ago)

4*4!=4 *24=96
5*5!=120*5=600 and all else numbers products ends with 00 so if we add we get 96 in tens and units place so 96%64 is the answer

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swati priya  (9 years ago)

the remainder will be 2+2=4

Is this solution Helpfull? Yes | No (1)  

Anuj Baranwal  (9 years ago)

Remainder of [ (4.4!+5.5!)/64 + (6.6!+7.7!+...........+19.19!)/64]
= Remaider of [(96+600)/64)] + Remainder of [( 6.6!+7.7!+...........+19.19!)/64)]
= 56 + 0
= 56

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