If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:3:20

GMAT: Data sufficiency 21 (correction)

Video transcript

Problem 94. In Jefferson School, 300 students study French or Spanish or both. OK. And they have to do one of those two. If 100 of these students do not study French-- so this sounds like a Venn Diagram. Let's see. So let's say that's French. And I'll do Spanish in a different color. Let's say that is Spanish. And we have 300 students, and they study either French or Spanish. If 100 of these students do not study French-- so what did I say? This was French and this is Spanish. So 100 of these students do not study French. So this area right here is 100. Right? Those are people who study Spanish but no French at all. How many of these students study both French and Spanish? So what they want to know is the intersection of who studies French and Spanish. So that's this blue area right here. So statement number one tells us, of the 300 students, 60 do not study Spanish. So people who study French but no Spanish-- and I didn't mean they know Spanish. People who study French and do not study Spanish, that's this right here. And that's 60. Right? And let's see if we can use this information to figure out what the intersection is. So if you think about it, what we want to do is the whole universe. So the whole universe is going to be equal to the people who study-- so this 60 people plus-- we'll call that the intersection, or we could call that French and Spanish-- plus this blue area, plus this tan area. Right? That's the whole universe. And that is equal to 300. So people who study French and Spanish plus 160 is equal to 300. Subtract 160 from both sides and you get the people who study just French and Spanish. That's what? That's 240. That's 140 people who study both French and Spanish. So statement one is sufficient. Let's see what statement two gets us. Statement two tells us, a total of 240 of the students study Spanish. So in statement two, we don't know this. But we know that a total of 240 students study Spanish, right? So we know that this whole circle is 240. And if we're just trying to figure out this blue part, we just have to subtract out the tan part. So if we want to know French and Spanish, French and Spanish is going to be equal to the whole amount that study Spanish-- which they just told us, 240-- minus just the people who study only Spanish. Right? Because you could study Spanish and French. So 240 people who study Spanish minus the people who just study Spanish. So that's 100. That's that tan area. That also equals 140. So both statements individually are sufficient to answer this question. So the answer is D.