Bunuel wrote:
When positive integer m is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above
Kudos for a correct solution.
This is a good question. The best approach to this question is via statements I, II, III:
I: 8 = \(2^3\) As 8 has 2 as its factor, all the multiple of 8 will be multiple of 2. Therefore, 3 can't be the unit digit of m*n if n=8.
II: 15 = \(3*5\) As 15 has 5 as its factor, all the multiple of 15 will have 5 or 0 as unit digit. Therefore, 3 can't be the unit digit of m*n if n=15.
III: 30 = \(2*3*5\) As 30 has 2 & 5 as its factor, all the multiple of 30 will have 0 as unit digit. Therefore, 3 can't be the unit digit of m*n if n=30.
Correct answer is E