IT Convention Discrete Math

Question

An IT convention was attended by 4,000 IT specialists. There are 2,000 Java programmers,1,900 SQL programmers and 1,800 PHP programmers. 800 are Java and SQL programmers, 900 are Java and PHP programmers, 600 are SQL and PHP programmers, and 500 are Java, SQL and PHP programmers. How many were Java, SQL or PHP programmers?

Answer 1

This is a set problem where you are tasked with finding the intersection of three sets. I would recommend drawing a Venn Diagram with three to visualize this (similar to the one seen here https://www.lucidchart.com/pages/tutorial/venn-diagram).

One circle represents PHP programmers, the next represents SQL programmers, and the last represents Java programmers. The overlapping areas represent the programmers who know multiple languages. Start by filling out the information that you do know and then look for what you can deduce based on that. Your eventual goal is to figure out how many programmers are in the center (the area that is included in all three circles).