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Sets

by mtripathy » Sun Sep 30, 2012 9:40 am
Source: OG 13th

In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study french, how many of these students study both French and Spanish?
(1) Of the 300 students, 60 do not study Spanish
(2) A total of 240 of the students study Spanish.

OA:D

I have tried to solve this problem with grids but get "E" as answer as both of the statements are insufficient. I am annexing herewith the grids for both statements which shows it is not possible to calculate X with the given data. Can any expert please explain?
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Source: — Data Sufficiency |

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by Ian Stewart » Sun Sep 30, 2012 10:11 am
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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by das.ashmita » Sun Sep 30, 2012 11:17 pm
Image

Hi mtripathy

In the question its mentioned, 300 students study French or Spanish or both.
Therefore, students studying none must be 0 as shown in the attached image.

With this info, both choices are suff. Hence D

Hope it s clear :)
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by mtripathy » Sun Sep 30, 2012 11:20 pm
Thanks Ian.
You are right in saying that we should be careful while using grids. In this problem there are zero students who study neither French nor Spanish. This data need to be filled in the grids to come out with right answer.
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