Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Two and Three-digit numbers.
Two and Three-digit numbers – AIME I, 1997
Sarah intended to multiply a two digit number and a three digit number, but she left out the multiplication sign and simply placed the two digit number to the left of the three digit number, thereby forming a five digit number. This number is exactly nine times the product Sarah should have obtained, find the sum of the two digit number and the three digit number.
- is 107
- is 126
- is 840
- cannot be determined from the given information
Check the Answer
But try the problem first…
Answer: is 126.
AIME I, 1997, Question 3
Elementary Number Theory by David Burton
Try with Hints
Let p be a two digit number and q be a three digit number
from factors of 1000 gives 9p-1=125
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