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# In Jefferson School, 300 students study French or Spanish or

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Senior Manager
Joined: 20 Feb 2006
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In Jefferson School, 300 students study French or Spanish or [#permalink]

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13 Dec 2006, 14:03
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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

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Joined: 08 Nov 2006
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Location: Ann Arbor
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13 Dec 2006, 14:16
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F+S-(F&S)=300

S=100(those who do not study french)

So equation is now,

F+100-(F&S)=300

(1) Of the 300 students, 60 do not study Spanish.
==> F=60.
Substituting this in the equation, we get F&S=140.So sufficient.

(2) A total of 240 of the students study Spanish
This means that 140 students study spanish and also french.
So sufficient.

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Senior Manager
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13 Dec 2006, 16:20
If 100 do not study French then doesn't that mean that 200 do study French?

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13 Dec 2006, 16:33
If 100 do not study French then doesn't that mean that 200 do study French?

Yes, but also consider that some of the 200 can also study spanish. If you want to identify the students who study only french, then you will need to exclude the spanish students from this group.
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Senior Manager
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13 Dec 2006, 19:57
If 100 do not study French then doesn't that mean that 200 do study French?

Yes, but also consider that some of the 200 can also study spanish. If you want to identify the students who study only french, then you will need to exclude the spanish students from this group.

Thanks! Was having a mental block.

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Manager
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15 Dec 2006, 18:49
st. fwd Q.

S U F = S+F-SnF
Stem gave: LHS=300 and only S =100..To find SnF

1) only F =60 ->

S =300-60=240
from stem, only S=100

->> S n F = 140 Suff...

2) S=240

from stem, only S =100
->> intersection = 140 Suff..

check this:
Given, Its either S or F or both ..therefore, you can see a picture mentally and pickup D in 5-10 secs

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Director
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06 Nov 2007, 18:19
Is there anyway to solve this using a table instead of a venn diagram?

For example:
...................French..............No French............Total

Spanish..........?...............................................240

No Spanish......................................................60

Total:............200....................100...................300

Using a table I got E. It is obviously wrong, but can you explain why a table of this soft won't work in this situation and a venn diagram is needed?

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Intern
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06 Nov 2007, 22:49
You can't use 300 as the total since 300 is people who studies French, Spanish, or BOTH.....the chart has a NEITHER column so you can't use 300 as the total.

F+100-(F&S)=300

(1) Of the 300 students, 60 do not study Spanish.
==> F=60.
Substituting this in the equation, we get F&S=140.So sufficient.

When I plug in the 60, I get 160-(FuS)=300 and a negative 140. Maybe it's late and I can't think but it shouldn't be a negative number.

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28 Nov 2007, 10:15
Witchiegrlie wrote:
You can't use 300 as the total since 300 is people who studies French, Spanish, or BOTH.....the chart has a NEITHER column so you can't use 300 as the total.

F+100-(F&S)=300

(1) Of the 300 students, 60 do not study Spanish.
==> F=60.
Substituting this in the equation, we get F&S=140.So sufficient.

When I plug in the 60, I get 160-(FuS)=300 and a negative 140. Maybe it's late and I can't think but it shouldn't be a negative number.

can someone clarify this ? i get a negative 140 with this formula as well (F+S-FS=300)

i do get a +140 with seeing S as S=100+SF (from the stem sayin 100=S-SF)

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28 Nov 2007, 10:15
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