Problem Solving

A local bank that has 15 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?

A 3
B 4
C 5
D 6
E 7

[spoiler]Ans: B. [/spoiler]

Let the minimum number of digits be x

Thus, total number of combinations (including repetitions) would be x^2

Now, we want x^2 to be atleast 15, thus x should be 4.

This question involves deciding how many things are available for each slot and then multiplying all of the slots together to get your answer. Since the question asks you for the least number of integers to make 15 codes it is best to look at the answers first, starting with the lowest - remember you can repeat digits in the code.

If there were 3 digits then the total number of codes would be 3(3) = 9 - too few
if there were four digits then the total number of codes would be 4(4) = 16 - this is at least 15 so B is the answer.