Latest Elitmus Aptitude Question SOLUTION: How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.

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(#M40030556) ELITMUS Numerical Ability question Asked in 24th Nov Test Keep an EYE

How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.

Asked In Elitmus Manmita Pattnaik (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

khushbu  (10 years ago)

720-72=648....100% SURE

Is this solution Helpfull? Yes (29) | No (3)  

Shaibal Dutta  (10 years ago)

when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
when 4 in units place, 64,24 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 3*4! ways.
when 5 in units place, no of ways 5! ways.
when 6 also ,it is 5! ways.

So totally answer is 5!+5!+5!+(2*4!)+5!+5!=648 ways........


@anchuri ur process ws crrct d only mstk u hv dn is dt u repeat 44 ...nd fr ds d ansr ws chngd ... gd 1 bro keep it up

Is this solution Helpfull? Yes (18) | No (2)  

Anchuri Sandeep Reddy  (10 years ago)

Sorry i have done one mistake in below submitted one....
when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
when 4 in units place, 64,24 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 2*4! ways.
when 5 in units place, no of ways 5! ways.
when 6 also ,it is 5! ways.

So totally answer is 5!+5!+5!+(2*4!)+5!+5!=648 ways........

Is this solution Helpfull? Yes (5) | No (1)  

Darshan  (10 years ago)

actually numbers are not be repeated.hence when unit digit is 4 ,the no of possible 6 digit no will be 48,hence we get 600+48=648

Is this solution Helpfull? Yes (4) | No (2)  

keshav  (10 years ago)

when unit digit will be 1 or 2 or 3 or 5 or 6 then all the numbers formed will be divisible by these numbers respectively.
by taking one of these numbers at unit place,other place can be filled by 5!
when unit digit will be 4, 10th place can be filled by 6 or 2 i.e 2 ways..other places can be filled by 4!
so, total numbers formed = 5*5!+2*4!=648

Is this solution Helpfull? Yes (4) | No (1)  

Manmita Pattnaik  (10 years ago)

optios-
a)360
b)648
c)660
d)720

Is this solution Helpfull? Yes (2) | No (1)  

alok chand  (10 years ago)

when unit digit = 1 ,then no. of way is 5!(last digit 5 is fixed and remaining initial 5 digits are can be rearrange b/w 5 places by 5! way).
so no. of way= 5!.
when unit digit =2, then no. way= 5!also
when unit digit = 3, (d sum of total no. is divisible by 3).and no. of way =5!
when unit digit =4,(and last two digits are 64 or 24 both are divisible by 4), no. of way =2*4!.
when unit digit =5, no of way= 5!.
when unit digit =6, no of way =5!(2*3=6,and the sequence is divisible by 2&3 both so also divisible by 6)
total no of way=(5!)+(5!)+(5!)+(2*4!)+(5!)+(5!)= 648.

Is this solution Helpfull? Yes (2) | No (1)  

mitthu kumar  (10 years ago)

when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
when 4 in units place, 64,24 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 8*4!(as last two digits will be 12,16,24,32,36,52,56,64) ways.
when 5 in units place, no of ways 5! ways.
when 6 also ,it is 5! ways.

So totally answer is 5!+5!+5!+(8*4!)+5!+5=768

Is this solution Helpfull? Yes (2) | No (3)  

ravi gangwar  (10 years ago)

anchuri why 44 is repition allowed.......

Is this solution Helpfull? Yes (2) | No   

Anchuri Sandeep Reddy  (10 years ago)

when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
when 4 in units place, 64,24,44 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 3*4! ways.
when 5 in units place, no of ways 5! ways.
when 6 also ,it is 5! ways.

So totally answer is 5!+5!+5!+(3*4!)+5!+5!=672 ways........

Is this solution Helpfull? Yes (1) | No (10)  

pavan  (10 years ago)

we can form 6! ways

so 6!=720

Is this solution Helpfull? Yes (1) | No (10)  

Sakshi  (10 years ago)

You have 6 choices for the units digit, leaving 5 choices for the tens digit, leaving 4 choices for the hundreds digit, and so on. In all, 6*5*4*3*2*1 different numbers.

Is this solution Helpfull? Yes (1) | No (4)  

riddhi soni  (10 years ago)

kahin se copy kiya h kya......every tyme @achuri u hv written same same....why dont u explain how...if 6 digit no. can be formed then how come 5!

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

ganachari nandini  (10 years ago)

hi for the no.to be divisible by 4 the condition is sum of last two digits is divisible by 4 then how 64 i.e..6+4=10 and 24 i.e..2+4=6 are not divisible by 4 can be considered please give the correct solution

Is this solution Helpfull? Yes | No (1)  

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