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number properties

by sud21 » Thu Jan 26, 2012 11:52 pm
When 2105 is multiplied by single digit integer m product has unit digit=5 and hundreds digit n. X is set of all values of m. Y is set of all values of n. What are the values for X & Y?
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by neelgandham » Fri Jan 27, 2012 6:55 am
When 2105 is multiplied by single digit integer m product has unit digit=5 and hundreds digit n. X is set of all values of m. Y is set of all values of n. What are the values for X & Y?

X = (1,3,5,7,9)- All odd numbers less than 10, produce integers with unit's digit 5 when multiplied to 2105
Y = (1,3,5,7,9) How? Strict multiplication

2105 * 1 = 2105 - (1)
2105 * 3 = 6315 - (2)
2105 * 5 = 10525((2)+(1)+(1)) - (3)
2105 * 7 = 14735((3)+(2)-(1)) - (4)
2105 * 9 = 18945((5)+(3)+(1))

Not sure of an easier way!
Anil Gandham
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