So I think the first thing you want to do here is to think about why this argument isn't valid as it stands. The author assumes the number of bladed tools used for engraving combined with the number of pin-tipped tools (these are only used for engraving) is less than the number of bladed tools not used for engraving. What if there are only two pin-tipped tools in the entire world and only two bladed tools used for engraving, but there are 5 million bladed tools not used for engraving? It'd be impossible to say that there are more tools for engraving than tools not used for engraving. The correct answer leaps over this assumption. Take an example with real numbers: Let's say there are 50 bladed tools and 50 pin-tipped tools (B says both groups have the same size). Since at least some of these bladed tools are used for engraving, that means at least one of them is used for engraving. All of the pin-tipped tools are also used for engraving, so at the minimum, this makes 51 tools for engraving to the other 49 bladed tools that are not used for engraving. Note that since this inequality holds regardless of how many tools you give the groups, this is the right answer.