Question

How many five digit numbers of the form xxyxx divisible by 33

Answer 1

Answer:

Well, 3 Numbers .

Step-by-step explanation:

Since it's a 5 digit number, x is an integer between 1 and 9.

form: xxyxx

Divisible by 33 ie. by 11 and 3.

11..: difference between sums of alternate digits is divisible by 11.

So x+y+x - (x+x) = 11 × a

Or y = 11 a for some integer a>=0.

This is only possible if y = a = 0.

3.. : sum of digits divisible by 3.

So 4x+y = 3 b for some integer b>0.

So 4 x = 3 b

ie. x is a multiple of 3.

So x = 3, 6, 9.

Answers: 33033, 699099 and 99099.

Answer 2

Answer:

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