What is the remainder when 123456789101112131415161718192021222324252627282930313233343536373839404142434481 is divided by 45?  Choose the most appropriate option: A) 26 B) 36 C) 16 D) 06 E) 40

Rationale: explanation : let ' s call : a = 123456789101112131415161718192021222324252627282930313233343536373839404142434481 = > a = b * 100 + 81 [ with b = 1234567 . . . . . 424344 ] we have : b x 100 is divisible by 45 because : - sum of all digits in b = 1 + 2 + 3 + . . . . + 44 = ( 1 + 44 ) + ( 2 + 43 ) + . . . . + ( 22 + 23 ) ( 22 pairs ) = 22 * 45 = > b divisible for 9 since b is divisible by 9 , b * 100 will be divisible by 9 * 5 = 45 81 divided 45 gives a remainder of 36 therefore , a divided by 45 reminder 36 answer : b
Answer: B