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

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Three hundred students at College Q study a foreign language. Of these  [#permalink]

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New post 27 Dec 2015, 08:56
2
8
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

64% (02:44) correct 36% (02:32) wrong based on 203 sessions

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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

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Re: Three hundred students at College Q study a foreign language. Of these  [#permalink]

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New post 29 Dec 2015, 10:39
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[quote="Bunuel"]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


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
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Re: Three hundred students at College Q study a foreign language. Of these  [#permalink]

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New post 29 Jan 2016, 05:09
peachfuzz wrote:
Bunuel wrote:
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


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


Hi, can you please elaborate on your approach? Why subtract 190-130 to get smallest amount that could study only spanish?
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Re: Three hundred students at College Q study a foreign language. Of these  [#permalink]

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New post 29 Jan 2016, 05:36
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1
lpetroski wrote:
peachfuzz wrote:
Bunuel wrote:
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


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


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


Look below for an explanation.

You are given

Attachment:
1-29-16 8-27-25 AM.jpg
1-29-16 8-27-25 AM.jpg [ 22.65 KiB | Viewed 2158 times ]


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.

Attachment:
1-29-16 8-28-57 AM.jpg
1-29-16 8-28-57 AM.jpg [ 26.1 KiB | Viewed 2159 times ]


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.

Attachment:
1-29-16 8-28-25 AM.jpg
1-29-16 8-28-25 AM.jpg [ 25.29 KiB | Viewed 2157 times ]


Thus, the range is 60-100.

Hence C is the correct answer.

Hope this helps.
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Re: Three hundred students at College Q study a foreign language. Of these  [#permalink]

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New post 29 Jan 2016, 05:55
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
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1.png [ 7.97 KiB | Viewed 2116 times ]

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Re: Three hundred students at College Q study a foreign language. Of these  [#permalink]

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New post 29 Jan 2016, 10:25
1
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
Overlapping sets.png [ 36.13 KiB | Viewed 2078 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
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Re: Three hundred students at College Q study a foreign language. Of these  [#permalink]

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