# GMAT Question of the Day – Problem Solving – Combinatorics/Number Properties

A certain company tags each of its products with an 8 digit alpha numeric code whose first 4 digits are either a digit 0-9 or a letter of the alphabet and whose last 4 digits represent the year of manufacture (for example, the last 4 digits of a product created in 2010 would be 2010). If letters and numbers may be repeated what is the maximum number of products that can be given a unique tag in any 3 year period?

A. 5,038,848

B. 3,020,176

C. 1,679,616

D. 1,513,692

E. 1,217,460

[spoiler]**A.**[/spoiler]

## GMAT Question of the Day Solution

Here is another challenging GMAT combinatorics question. If you have a good basic understanding of ordering this question of the day shouldn’t be too difficult. The most difficult part is understanding the parameters of the question. What are the rules for the code? Once you’ve done that this is a basic ordering question (for my GMAT tutoring students I recommend a simple slot method which you can see in the explanation diagram) with just one more twist: The numbers are huge! Whenever you have a seemingly impossible calculation the GMAT will help you out with a shortcut. One to look out for – units digit. You can do some quick and dirty units digit math and see that only one answer choice has the appropriate units digit.