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

Question

Three hundred students at College Q study a foreign language. Of these, 110 of those students study French, and 170 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from

A. 10 to 40
B. 40 to 100
C. 60 to 100
D. 60 to 110
E. 70 to 110

Show Answer

Official Answer

C

A. 10 to 40 
B. 40 to 100 
C. 60 to 100 
D. 60 to 110 
E. 70 to 110

ENGRTOMBA2018 · Accepted Answer

Look below for an explanation. You are given 1-29-16 8-27-25 AM.jpg Text in red is the 'calculated' value, text in black is the given information. 'x' denotes the quantity that we need to calculate. As shown in, you are told that ATLEAST 90 students study neither French nor Spanish. Thus for calculating the range for Students that study Spanish and NOT French, you need to assume both the minimum and maximum values. Minimum value = 90 while maximum is dictated by 130 students not studying Spanish (=130). Put these values 1 by 1 as shown below to calculate the range. When you put Not Spanish and Not French = 90, you get Spanish and NOT French as = 190-90=100. This is the upper bound of the students asked. 1-29-16 8-28-57 AM.jpg When you put Not Spanish and Not French = 130, you get Spanish and NOT French as = 190-130=60. This is the lower bound of the students asked. 1-29-16 8-28-25 AM.jpg Thus, the range is 60-100. Hence C is the correct answer. Hope this helps.

peachfuzz · Answer

Three hundred students at College Q study a foreign language. Of these, 110 of those students study French, and 170 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from

A. 10 to 40
B. 40 to 100
C. 60 to 100
D. 60 to 110
E. 70 to 110

Show Answer

Official Answer

C

110 students study French
190 students do not study French

170 students study Spanish
130 students do not study Spanish

90 students study neither French nor Spanish

190-130=60
190-90=100

C. 60 to 100

lpetroski · Answer

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

vivekkumar987 · Answer

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

davedekoos · Answer

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.

Attachment:

Overlapping sets.png [ 36.13 KiB | Viewed 10941 times ]

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

Rovina23 · Answer

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

bumpbot · Answer

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

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