Three hundred students at College Q study a foreign language. Of these

Hi, can you please elaborate on your approach? Why subtract 190-130 to get smallest amount that could study only spanish?

QUICK APPROACH TO THE SUM:

STEP 1 : WE CAN FIND THE MAXIMUM VALUE BY MINIZING S/ & F/ ( THE MINIMUM VALUE IS 90, SO THE MACIMUM VALE WILL BE 100 FOR S & F/

SO WE COME DOWN TO OPTION B & C , REST ARE ELIMINATED

STEP 2 :
WE HAVE TO JUST 40 & 60 IN THE BOXES ONLY 60 CAN SATISFY

SO IMO is C

For problems like this with overlapping sets where numbers can shift (at least 90 students...), I like to use a graphical approach so I can visualize what is going on.



In the first part, there are 90 students taking neither Spanish nor French, which leaves 210 students who take either Spanish or French or both. To maximize the number of students who take Spanish but not French, we will minimize the overlap of the two classes. Here we see that there can be a maximum of 100 students who take Spanish but not French.

In the second part, to minimize the number of students who take Spanish and not French, we should maximize the overlap of the two sets. The French students get shifted to the left by 40 so that every student who takes French also takes Spanish. Now there are 130 students who take neither Spanish nor French, and a minimum of 60 who take Spanish but not French. You can see that you can't reduce the number below 60, because no matter where you slide the french students, there will always be 60 who take Spanish and not French.

Answer: C

Total students studying a foreign language = 300
Not Spanish Not French is > or = 90 (let's assume it to be 90 since it must be at least 90)

Remaining students = 210

French and Spanish = x
French Alone = 110-x
Spanish Alone = 170-x

210 = 110-x + x + 170-x
x = 280-210
x > or = 70 (70 is the least value that x can be since we assumed the least value for not french not spanish i.e. 90)
Therefore, Only Spanish = 170 - x = 100 (This is the greatest value)

Assume there are no french only students, the greatest value both French and Spanish can be is 110.

Therefore only Spanish = 170-110 = 60

Hence, Range of only Spanish students = (c) 60 to 100

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