Amit multiplied a 3-digit number by 1002 and got AB007C, where A, B, and C stand for digits. What was Amit's original 3-digit number?
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Let the required number be 1 0 0 x + 1 0 y + z , where x , y , z are the digits of the number. Then 2 0 y + 2 z = 7 0 + C . Since z can't be greater than 9 , therefore y = 3 , z = 2 C + 5 . Also, from the given conditions, 2 0 0 x + 1 0 0 0 z ≥ 1 0 0 0 0 (since the hundred's and thousand's place digits of the product are both zero). Since z m a x = 9 and 2 0 0 x ≤ 1 8 0 0 , therefore x = 5 and z = 9 , and the required number is 5 × 1 0 0 + 3 × 1 0 + 9 = 5 3 9