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GMAT: Data sufficiency 21 (correction)

Video transcript

problem 94 in Jefferson school 300 students study French or Spanish or both okay and they have to do one of those two if 100 of these students did not say French so this sounds like a Venn diagram see draw so let's say that's French and I'll just vanish in a different color let's say that is Spanish and we have 300 students and they study either French or Spanish if a hundred of these students do not study French so what did I say this was French and this is Spanish so a hundred of these students do not study French so this area right here is a hundred right those are people who study Spanish but no French at all how many of these students study both French and Spanish so that 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 of the 360 do not study Spanish so essentially this area right here let me see if I could so people who study French but know Spanish and not that I mean they know Spanish people who study French and do not study Spanish that's this right here and that's 60 all 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 this 60 people right plus we'll call that the intersection or we can call that French and Spanish right 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 divide 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 studied both French and Spanish so statement one is sufficient let's see what statement 2 gets us statement 2 tells us a total of 240 of the students study Spanish so statement 2 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 the 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 - the people who just study Spanish so that's 100 that's that 10 area that also equals 140 so both statements individually are sufficient to answer this question so the answer is D