GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In a class of 25 students, each student studies either Spani
[#permalink]
05 Aug 2018, 14:42
05 Aug 2018, 14:42
1
Expert Reply
10
Bookmarks
00:00
Question Stats:
51% (01:26) correct
48% (01:34) wrong based on 195 sessions
Hide Show timer Statistics
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
[#permalink]
07 Aug 2018, 16:52
07 Aug 2018, 16:52
5
Expert Reply
1
Bookmarks
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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In a class of 25 students, each student studies either Spani
[#permalink]
20 Aug 2020, 09:49
20 Aug 2020, 09:49
9
3
Bookmarks
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
