Find the number of six digit numbers of the type ababab that is divisible by 148. Given that a≠b.

The answer is 20.

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The 6 digit number is of the form ababab.

We can represent such a number as 10101×pq where pq is a two digit number. (For better understanding taking the simple example 10101×24=242424 or any in this manner)

prime factorising 10101 = 3×7×13×37 prime factorising 148 = 2×2×37

Clearly 10101 cannot be divided by 4 thus the specific two digit number should be divisible by 4. ie, pq ∈ (4,8,12,16....96) which amounts to 24 numbers

But going back to the question it is clearly mentioned that a≠b so p≠q (10101× aa =aaaaaa) Also this only works for 2 digit numbers. So we subtact four of such cases which are 44,88,4 and 8.

Thus the final answer is 20.