Latest TCS Aptitude Question SOLUTION: How many 9 digit numbers are possible by using digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed? a.5^7 b.5^6 c.5^9 d.5^8

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How many 9 digit numbers are possible by using digits 1,2,3,4,5 which are divisible by 4 if the repetition is allowed?
a.5^7 b.5^6 c.5^9 d.5^8

Solution

_ _ _ _ _ _ _ _ _ (9 digit number)
Digits that can be used = 1, 2, 3, 4 and 5
For a number to divisible by 4, the last two digits have to be divisible by 4
So, the units digit cannot be 1, 3 or 5
If the units digit is 2, only 12, 32 adn 52 are acceptable as the last two digits
If the units digit is 4, only 24 and 44 are acceptable as the last two digits.
So, total 5 cases 12,24,32,44,52 are possible for the last two digits.
Now, the first 7 digits of the 9 digit number can be filled in 5^7 ways as each place can be filled by 1, 2, 3, 4 or 5.
So, desired answer = 5^7*5 = 5^8
This answer is given by Amitesh kumar and is right

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Asked In TCS sankha chowdhury (12 years ago)

Solved Moumita Ghosh Read Solution (3)

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Read Solution (3) :

Moumita Ghosh  (12 years ago)

i cant understand how this optins are possible......

anyway,the rule is any number divisible by 4 and constructed by 1,2,3,4,5 must have the last digits as 12,24,32,44,52.
so the last two digits can be any of these 5s
and the remaining 7 digits can be formed using 1,2,3,4,5 in any way
so 5*5*5*5*5*5*5*5(the last five is for the last two digits).

Is this solution Helpfull? Yes (7) | No (2)  

KUMAR SOUVIK MAJI  (12 years ago)

ya moumita is correct..option should be 5^8...not 58..

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

Ambika Prasad Tiwari  (12 years ago)

the options are incorrect
the answer wull be=5*5*5*5*5*5*5*5

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

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