Question

For how many two- digit positive numbers will tripling the tens digit give us a two-digit number that is triple the original number?

Answer 1

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/