Those grids do work if you know how to use them, but they're never necessary. I personally really dislike them and would never choose to use them; I'd always use a Venn diagram instead. It's much easier to tell how many unknowns you have looking at a Venn diagram, and it's also visually much easier to tell at a glance what any of your unknowns represent in more complicated problems.
From Statement 1 we learn that 60 students study *only* French. That leaves 240 students who study Spanish. Since, from the question stem, 100 study *only* Spanish, the rest, or 140, must study both Spanish and French.
You might see that Statement 2 gives identical information to Statement 1, so must be sufficient, or you can see that since 240 students study Spanish, and 100 study *only* Spanish, then 240 - 100 = 140 students must study both languages.
Just drawing the Venn diagram lets you see why the information is sufficient even more quickly.
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