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

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sandy
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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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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.
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C
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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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GreenlightTestPrep
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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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GreenlightTestPrep
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post   22 Sep 2021, 04:26
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Optimist wrote:

"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:"

What if french is 2 & 2 (intersection points with latin and Spanish) instead of the 2 & 1 you'd taken?
@Brent GreenlightTestPrep


If we distribute the five students who study exactly two languages in the way you suggest, we get:
Image

As you can see, still get 14 students studying French.

If you try other configurations, you'll still get 14 students studying French
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post   16 Jul 2019, 13:42
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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.


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   21 Sep 2021, 21:35
GreenlightTestPrep wrote:
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


"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:"

What if french is 2 & 2 (intersection points with latin and Spanish) instead of the 2 & 1 you'd taken?
@Brent GreenlightTestPrep
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post   25 Jan 2022, 22:50
Hi, how did you come up with 2-2-1? what about 1-1-3?

GreenlightTestPrep wrote:
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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GreenlightTestPrep
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post   26 Jan 2022, 06:37
1
Chaithraln2499 wrote:
Hi, how did you come up with 2-2-1? what about 1-1-3?


Once we get to this point....
Image
... we can place the 5 students (i.e., the 5 students who study exactly two languages) and the overlap areas in many different ways.
One option is 2-2-1.
Another option is 3-0-2
Another option is 1-1-3

Regardless of which option we choose, we will always get 14 students studying French.
Try it.
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beretta
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post   22 Apr 2023, 11:19
Can someone solve this question with a double matrix method?
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Re: In a class of 25 students, each student studies either Spani [#permalink] New post   22 Apr 2023, 16:20
Expert Reply
This kind of problem cannot be solved efficiently with the double matrix. They have three area to work and set up.

a double matrix is best when you do have two mutually exclusive choices such as : a car with wind shield or not and with aircon or not.
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