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In a class of 25 students, each student studies either Spani

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In a class of 25 students, each student studies either Spani [#permalink] New post 05 Aug 2018, 14:42
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Question Stats:

57% (01:17) correct 42% (01:13) wrong based on 97 sessions
In a class of 25 students, each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages. 9 study Spanish, 7 study Latin, and 5 study exactly two languages.

Quantity A
Quantity B
The number of students who study French
14


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Retired Moderator
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post 07 Aug 2018, 16:52
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Explanation

The problem specifies that no one studies all three languages. In addition, a total of 5 people study two languages.

Thus, 5 people have been double-counted. Since the total number of people who have been double-counted (5) and triple-counted (0) is known, use the standard overlapping sets
formula:

Total = Spanish + French + Latin – (Two of the three) – 2(All three)
25 = 9 + French + 7 – 5 – 2(0)
25 = 11 + French
14 = French

The two quantities are equal.
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post 16 Jul 2019, 13:42
sandy wrote:
In a class of 25 students, each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages. 9 study Spanish, 7 study Latin, and 5
study exactly two languages.

Quantity A
Quantity B
The number of students who study French
14


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Expect a better explanation from GreenLightTestPrep sir.
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post 18 Aug 2020, 18:50
sandy wrote:
Explanation

The problem specifies that no one studies all three languages. In addition, a total of 5 people study two languages.

Thus, 5 people have been double-counted. Since the total number of people who have been double-counted (5) and triple-counted (0) is known, use the standard overlapping sets
formula:

Total = Spanish + French + Latin – (Two of the three) – 2(All three)
25 = 9 + French + 7 – 5 – 2(0)
25 = 11 + French
14 = French

The two quantities are equal.




This reasoning makes no sense to me. Here is what I had done previously in a group of 25 students we know that 9 study Spanish, 7 study Latin, and 5 students study 2 of the 3 languages. So therefore, if we assume different combinations for them ex.) Latin/French or Spanish/French or Latin/Spanish then the maximum possible # of students for French can range from 9 to 4 which is still less than 14. Which would make the correct answer B. Where did I go wrong in my logic?
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post 20 Aug 2020, 09:49
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sandy wrote:
In a class of 25 students, each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages. 9 study Spanish, 7 study Latin, and 5 study exactly two languages.

Quantity A
Quantity B
The number of students who study French
14


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


I'm not a big fan of memorizing formulas, so here's a way to solve the question using diagrams.
We're going to start from the center and work our way out.

Each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages.
First we can place 0 in the intersection of all three circles.
Image



5 study exactly two language
Since we aren't told that the distribution of those five students who study exactly two languages, we can distribute them anyway we want.
Here's one option:
Image



9 study Spanish, 7 study Latin
We'll add 5 and 4 in order to meet the conditions above
Image


There are 25 students in the class
So far, we've accounted for 14 of the 25 students.
So the remaining 11 students must study only French
Image

So the TOTAL number of students studying French = 2 + 0 + 1 + 11 = 14

We get:
Quantity A: 14
Quantity B: 14

Answer: C

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: In a class of 25 students, each student studies either Spani   [#permalink] 20 Aug 2020, 09:49
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