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Question 671627: I am a three digit number less than 300. I am divisible by two and five but not by three. My first digit is smaller than my second digit and the sum of my digits is four. What number am I?
Found 2 solutions by DrBeeee, MathTherapy:
Answer by DrBeeee(684)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! I am a three digit number less than 300. I am divisible by two and five but not by three. My first digit is smaller than my second digit and the sum of my digits is four. What number am I?
Since the number is divisible by 2 and 5, but not 3, then the units digit MUST be 0
Let hundreds digit be H, tens digit, T, and units digit, U
Then: 100H + 10T + U < 300 ------- 100H + 10T + 0 < 300 ------ 100H + 10T < 300 ------ (i)
H < T ------- (ii)
H + T + U = 4 ------- T = 4 H 0 ------ T = 4 H ------- (iii)
100H + 10T < 300 ------- (i)
100H + 10(4 H) < 300 ------- Substituting 4 H for T in (i)
100H + 40 10H < 300
90H < 260 ----- 10(9H) < 10(26)
9H < 26 -----  , or 
H < T ----- (ii)
H < 4 H ------- Substituting 4 H for T in (ii)
H + H < 4
2H < 4
 , or 
This means that H MUST = 
T = 4 H ------- (iii)
T = 4 1 ----- Substituting 1 for H
Since H, or hundreds digit = 1, T, or tens digit = 3, and U, or units digits = 0, then 3-digit number = 
Do the check to see if all the clues match up!!
Send comments and thank-yous to D at MathMadEzy@aol.com
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