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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
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 Please feel free to post as many doubts on our discussion forum as you can. If you find any questionDifficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best Jayati!!!Regards,Askiitians ExpertsPriyansh Bajaj
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
Please feel free to post as many doubts on our discussion forum as you can. If you find any questionDifficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best Jayati!!!Regards,Askiitians ExpertsPriyansh Bajaj
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