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# Four of the students applying to schools this year are applying only

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Posts: 51280
Four of the students applying to schools this year are applying only  [#permalink]

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22 Mar 2017, 02:40
00:00

Difficulty:

55% (hard)

Question Stats:

70% (02:16) correct 30% (02:45) wrong based on 224 sessions

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Four of the students applying to schools this year are applying only to schools on the west coast and to schools on the east coast, 6 of the students are applying only to schools on the west coast and to schools in the south, and 5 of the students are applying only to schools on the east coast and schools in the south. If 5 of the students apply to schools in all 3 regions, how many of the 45 students applied to schools in only one region?

A. 5
B. 10
C. 20
D. 25
E. 30

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Re: Four of the students applying to schools this year are applying only  [#permalink]

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22 Mar 2017, 08:07
1
Let Total Number of Students applying to schools in only one region = S
Let Total Number of Students applying to schools in Two regions = B = 4+6+5 = 15
Let Total Number of Students applying to schools in Three regions = T =5

Total Number of Students = S+B+T = 45
S=45 -B-T = 45 -20 = 25

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Four of the students applying to schools this year are applying only  [#permalink]

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22 Mar 2017, 21:24
Bunuel wrote:
Four of the students applying to schools this year are applying only to schools on the west coast and to schools on the east coast, 6 of the students are applying only to schools on the west coast and to schools in the south, and 5 of the students are applying only to schools on the east coast and schools in the south. If 5 of the students apply to schools in all 3 regions, how many of the 45 students applied to schools in only one region?

A. 5
B. 10
C. 20
D. 25
E. 30

In order to solve this question we need to subtract the total numbers of students by both the sum of three groups that apply to two schools only and the group(s) that apply to three schools. For simplicity, we can draw a venn diagram- it is important to note that the statement "four of the students applying to schools this year are applying only to schools on the west coast and schools on the east coast" does not mean that the number of students applying to only schools in those regions are four and four- this is a comprehension mistake I made at first.
Attachments

Scan0.pdf [449.04 KiB]

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Posts: 533
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Re: Four of the students applying to schools this year are applying only  [#permalink]

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23 Mar 2017, 02:38
1
Top Contributor
Hi,

It’s always better to use the Venn-Diagram for any overlapping set questions, this gives more clarity,

Given,

Number of students who applied west and east = 4

Number of students who applied west and south = 6

Number of students who applied east and south = 5

All three = 5

Totally 45 students who has applied for the schools

Note: Here few students might think, why we didn’t consider the neither case? We no need to think about the neither case, because we are solving for only “Students who
have applied”

From the diagram we can see that, the shaded part is what we have to find?

So the answer has to be 45 –(4+6+5+5) = 25

Hope this helps.
Attachments

Set theory.png [ 11.7 KiB | Viewed 1736 times ]

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Re: Four of the students applying to schools this year are applying only  [#permalink]

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23 Mar 2017, 03:31
1
Bunuel wrote:
Four of the students applying to schools this year are applying only to schools on the west coast and to schools on the east coast, 6 of the students are applying only to schools on the west coast and to schools in the south, and 5 of the students are applying only to schools on the east coast and schools in the south. If 5 of the students apply to schools in all 3 regions, how many of the 45 students applied to schools in only one region?

A. 5
B. 10
C. 20
D. 25
E. 30

Total Students Applying = Students applying to schools in exactly one region + Students applying to schools in exactly 2 regions + Students applying to schools in all 3 regions

45 = Students applying to schools in exactly one region + 4 + 6 + 5 + 5

Students applying to schools in exactly one region = 25

Check out the explanation of various overlapping sets formulas here: https://www.veritasprep.com/blog/2015/1 ... ping-sets/
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Re: Four of the students applying to schools this year are applying only  [#permalink]

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23 Mar 2017, 13:29
CrackVerbalGMAT wrote:
Hi,

It’s always better to use the Venn-Diagram for any overlapping set questions, this gives more clarity,

Given,

Number of students who applied west and east = 4

Number of students who applied west and south = 6

Number of students who applied east and south = 5

All three = 5

Totally 45 students who has applied for the schools

Note: Here few students might think, why we didn’t consider the neither case? We no need to think about the neither case, because we are solving for only “Students who
have applied”

From the diagram we can see that, the shaded part is what we have to find?

So the answer has to be 45 –(4+6+5+5) = 25

Hope this helps.

Hi,
How did you get your attachment to display? I drew the same diagram but cannot get it to display.
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Re: Four of the students applying to schools this year are applying only  [#permalink]

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23 Mar 2017, 15:55
1
1
Bunuel wrote:
Four of the students applying to schools this year are applying only to schools on the west coast and to schools on the east coast, 6 of the students are applying only to schools on the west coast and to schools in the south, and 5 of the students are applying only to schools on the east coast and schools in the south. If 5 of the students apply to schools in all 3 regions, how many of the 45 students applied to schools in only one region?

A. 5
B. 10
C. 20
D. 25
E. 30

We can create the following equation:

# of people applying = # applying in 1 region + # applying in 2 regions + # applying in 3 regions + # applying in 0 regions

Since 4 are applying only to schools on the west coast and to schools on the east coast, 6 of the students are applying only to schools on the west coast and to schools in the south, and 5 of the students are applying only to schools on the east coast and schools in the south, 4 + 6 + 5 = 15 students are applying to schools in 2 regions.

We are also given that 5 students apply to schools in all 3 regions and that the total number of students is 45. Since all students apply to schools in at least one of the regions, the number of students who apply to 0 regions is 0. We can let n = the number of students applying to a school in just one region and determine n:

45 = n + 15 + 5 + 0

25 = n

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Re: Four of the students applying to schools this year are applying only  [#permalink]

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03 Jul 2017, 12:41
What's the name of this type of quant question (using Venn diagram and involving overlapping counting, including this question and more advanced questions)?

Thanks
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Re: Four of the students applying to schools this year are applying only  [#permalink]

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03 Jul 2017, 19:47
2
kimrani wrote:
What's the name of this type of quant question (using Venn diagram and involving overlapping counting, including this question and more advanced questions)?

Thanks

These are "overlapping sets" questions.
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Four of the students applying to schools this year are applying only  [#permalink]

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07 Jul 2017, 14:35
VeritasPrepKarishma wrote:
kimrani wrote:
What's the name of this type of quant question (using Venn diagram and involving overlapping counting, including this question and more advanced questions)?

Thanks

These are "overlapping sets" questions.

Thanks a lot!

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Please give a kudos if you find this post useful.
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Joined: 22 Oct 2016
Posts: 22
Four of the students applying to schools this year are applying only  [#permalink]

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18 Jul 2017, 06:40
Hi Bunuel/ Karishma,

From 'how many of the 45 students applied to schools in only one region?', do we need to find at least 1 region or exactly 1 region.?

n(At least one set) = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C)
n(Exactly one set) = n(A) + n(B) + n(C) – 2*n(A and B) – 2*n(B and C) – 2*n(C and A) + 3*n(A and B and C)

Also, can the Exactly one set formula can be written as below.?
n(Exactly one set) = n(A) + n(B) + n(C) -2(d+e+f) +3(g)

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Re: Four of the students applying to schools this year are applying only  [#permalink]

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19 Oct 2017, 04:34
I originally approached this problem by performing the following calculations: 40-4+6+5+2(5)=20 and got the problem wrong. After reading other poster's answers I see how the answer is 25, however, I'm a little confused as to why we don't multiply the amount of students applying to schools in all three regions by two. Is it because the question prompt already accounts for any overlap? Thank you for your help.
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Re: Four of the students applying to schools this year are applying only  [#permalink]

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19 Oct 2017, 21:41
1
imranmah wrote:
I originally approached this problem by performing the following calculations: 40-4+6+5+2(5)=20 and got the problem wrong. After reading other poster's answers I see how the answer is 25, however, I'm a little confused as to why we don't multiply the amount of students applying to schools in all three regions by two. Is it because the question prompt already accounts for any overlap? Thank you for your help.

When dealing with numbers depicting "exactly" sets, there is no overlap in them.

Attachment:

SetsThree_1_23Sept.jpg [ 20.19 KiB | Viewed 704 times ]

This question gives us values for d, e, f and g.
We need the value of (a +b + c). We have already segregated each section and hence there is no overlap.
If instead the question gives us value of "Set A", "Set B" etc, there are regions which have overlap (d and g overlap in Set A and Set B) etc.

Check these posts:
http://www.veritasprep.com/blog/2012/09 ... ping-sets/
https://www.veritasprep.com/blog/2015/1 ... ping-sets/

They show how to handle overlapping sets questions.
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Re: Four of the students applying to schools this year are applying only  [#permalink]

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19 Oct 2017, 22:55
1
sarugiri wrote:
Hi Bunuel/ Karishma,

From 'how many of the 45 students applied to schools in only one region?', do we need to find at least 1 region or exactly 1 region.?

n(At least one set) = n(A) + n(B) + n(C) – n(A and B) – n(B and C) – n(C and A) + n(A and B and C)
n(Exactly one set) = n(A) + n(B) + n(C) – 2*n(A and B) – 2*n(B and C) – 2*n(C and A) + 3*n(A and B and C)

Also, can the Exactly one set formula can be written as below.?
n(Exactly one set) = n(A) + n(B) + n(C) -2(d+e+f) +3(g)

"only one region" means "exactly one region".
Check out the link above for all overlapping sets related formulas.
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Four of the students applying to schools this year are applying only  [#permalink]

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19 Oct 2017, 23:06
Can you explain why we don't multiply the students who applied to all three regions by two?
Four of the students applying to schools this year are applying only &nbs [#permalink] 19 Oct 2017, 23:06
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