Question

mark.
1.
The number of 6 digit numbers of the form "ABCABC", which are divisible by 13. where A. B
and C are distinct digits. A and C being even digits is
A) 200
B) 250
C) 160
D) 128​

Answer 1

Answer:

160

Step-by-step explanation:

because it is divisible by 13

Answer 2

Answer:

D - 128

Step-by-step explanation:

Consider the number as - ABC

Now we need to make ABC from ABCABC.

ABC x 1000 = ABC000

ABC000 + ABC = ABCABC

Which means (ABC x 1000) + ABC = ABCABC

∴ ABC . 1001 = ABCABC

Now, 1001 = 13 x 11 x 7

This means all possible values of ABCABC is divisible by 13, 11 and 7.

Now, possible combinations of ABC.

A & C are even digits.

A, B, C are distinct digits.

Possible values of A - 2, 4, 6, 8 - 4

Possible values of C - 0, 2, 4, 6, 8 - 5

Case 1 :- C = 0, Combinations A & C - 4. Here possible values of B - 8 (Since B is different from A & C) - 32

Case 2 :- C ≠ 0, Combinations A & C - 4 - 4 x 3. Here possible values of B - 8 (Since B is different from A & C) - 4 x 3 x 8 = 96

Possible combinations - 96 + 32 = 128