This is called a math problem

Algebra Level 2

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?

529 682 1002 539

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1 solution

Let the required number be 100 x + 10 y + z 100x+10y+z , where x , y , z x, y, z are the digits of the number. Then 20 y + 2 z = 70 + C 20y+2z=70+C . Since z z can't be greater than 9 9 , therefore y = 3 , z = C 2 + 5 y=3,z=\dfrac{C}{2}+5 . Also, from the given conditions, 200 x + 1000 z 10000 200x+1000z\geq {10000} (since the hundred's and thousand's place digits of the product are both zero). Since z m a x = 9 z_{max}=9 and 200 x 1800 200x\leq {1800} , therefore x = 5 x=5 and z = 9 z=9 , and the required number is 5 × 100 + 3 × 10 + 9 = 539 5\times {100}+3\times {10}+9=\boxed {539}

Thankyou sir.

Harsh Chaudhari - 1 year, 7 months ago

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