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In a class of 25 students, each student studies either Spani
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05 Aug 2018, 14:42
05 Aug 2018, 14:42
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Question Stats:
51% (01:26) correct
48% (01:34) wrong based on 197 sessions
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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.
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.
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.
Re: In a class of 25 students, each student studies either Spani
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07 Aug 2018, 16:52
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.
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
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20 Aug 2020, 09:49
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.
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.
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.
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:
9 study Spanish, 7 study Latin
We'll add 5 and 4 in order to meet the conditions above
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
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
