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by sud21 » Sat Jan 28, 2012 11:13 pm
When 3305 multiply one digit integer x, the product is a 5-digit integer with units' digit 5. The hundreds' digit of the integer is y, how many (x,y) are there?
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by Anurag@Gurome » Sat Jan 28, 2012 11:19 pm
sud21 wrote:When 3305 multiply one digit integer x, the product is a 5-digit integer with units' digit 5. The hundreds' digit of the integer is y, how many (x,y) are there?
When 3305 is multiplied with any odd one digit integer, the product will be an integer with unit's digit 5. But 3305*1 = 3305, a 4-digit integer.

When 3305 is multiplied with any odd one digit integer greater than 1 (3, 5, 7, and 9), the product will be an 5-digit integer with unit's digit 5.

Hence, there are four possible values for x.
And for each x there will be only one unique value of y.

Hence, four (x, y) are possible.
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