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Ventricate
For how many two- digit positive numbers will tripling the tens digit give us a two-digit number that is triple the original number?
I set this up as 10*a+b represents a 2 digit number (a needs to be multiplied by 10 because of the tens place. So If we triple the tens digit 3*10a + b or 30a+b = the new number with the 10's digit tripled so 30a+b = 3(10a+b) solved 30a+b = 30a + 3 b b = 3b 0=b this means a can be any digit as long as b = 0 10 * 3 = 30 20 * 3 = 60 30* 3 = 90 but 40 * 3 = 120, we no longer have a 2 digit number. I'm thinking 3 numbers is the answer. This discussion is out here also: http://www.takegmat.com/index.php/gmat-question-of-the-day-number-theory/