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Jayati Dinesh Bharadwaj Grade: 10
        


number of values of 'a'(from 0 to 9) for which the no N = 2345631143a4 is divisible by 12 is:


0, 1, 2,more than 2


i know the ans is 2.. plz explain.thanks in advance


6 years ago

Answers : (1)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
										


Dear Jayati,


Solution:- For the number to be divisible by 12, it has to be divisible by 4 and 3.


Divisibility criteria for 3: Sum of the digits of the number should be divisible by 3.


Sum of the digits of N = a + 36


Since, 36 is divisible by 3. So, for N to be divisible by 3, 'a' can have following values- 0, 3, 6, or 9.


Now, Divisibility criteria for 4: The last 2 digits of the number should be divisible by 4. In our case, 'a4' should be divisible by 4.


'a4' can be 04, 34, 64, or 94. From these 4 values, only 4 and 64 are divisible by 4. Therefore, 'a' can be either 0 or 6.


ANS = 2


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All the best Jayati!!!

Regards,
Askiitians Experts
Priyansh Bajaj


6 years ago
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