Latest TCS Aptitude Question SOLUTION: By using 1,2,3,4,5, how many 12 digit no. can be formed which is divisible by 4, repetation of no. is allowed?

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By using 1,2,3,4,5, how many 12 digit no. can be formed which is divisible by 4, repetation of no. is allowed?

Asked In TCS Deepak Dhanvantri (13 years ago)

Solved blingamurthy Read Solution (5)

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rajkumar  (13 years ago)

there are 12 places,its said tat the no. must be divisible 4 ,therfore last two digit must be divisible by four...ie it can be 12 or 24 or 32 or 44 or 52 only five ways are possible.....and now about first 10 digit repetation allowed,so it can be arranged in 5^10 ways... totally (5^10)*5=5^11 ways we can form 12 digit no tat is divisible by 4...
ans 5^11

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Aman  (13 years ago)

For a number to be divisible by 4 the last two digits of the no has to be divisible by 4:
hence using the above digits the last 2 digits of the no will be 12 32 52 24 44

hence keeping the two digits fixed the remaining digits can be filled in 5^10 ways
hence total no of numbers possible= (5^10)*5=5^11=48828125

Is this solution Helpfull? Yes (4) | No   

blingamurthy  (13 years ago)

For a number to be divisible by 4, the number formed by its last two digits must be divisible by 4. In this case, the only possibilities of last two digits divisible by four are 12, 24, 32, 44 and 52. The first 10 digits can be in any order. Thus, the answer is 5 times the number of 10 digit numbers that can be formed by using 1,2,3,4 and 5, which is 5^10 or 9,765,625
Therefore, the answer is 9,765,625 * 5 or 48,828,125.

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

Karthik Pandiyan  (13 years ago)

Let the number be of form ABCDE
Hence last two digit is divisible by 4 are 12,24,32,44,52
Hence first 10 digits can have values from 1-5
5^10 * 5= 5^11=48828125

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Som  (13 years ago)

5^11

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