A three-digit number is multiplied by a two-digit number whose tens’ digit is 9. The product is a four-digit number whose hundreds digit is 2. How many three-digit numbers satisfy this condition?
1 Answer
There are four 3-digit numbers that meet the conditions: 100, 101, 102, 103
Explanation:
Let's set up the question this way:
We have a 2-, 3-, and 4- digit number to discuss.
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The 2-digit number has a 9 in the tens digit, so it's the numbers 90 through 99
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The 4-digit number has a 2 in the hundreds place.
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The 3-digit number is any 3-digit number (100 through 999)
I want to get a sense as to what we're working with, so let's set the 2 and 3 digit numbers to the smallest and largest values and see what we get:
Smallest
And we can stop here - we've just eliminated most of the 4-digit numbers. We now know we want to look at 4-digit numbers starting with 92XX.
I think the easiest way to do this is to chart out a multiplication table in the ranges of numbers we're looking at:
And this shows us the final result - there are four 3-digit numbers that meet the conditions: 100, 101, 102, 103