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25 Mar 2024, 18:09
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
70% (01:41) correct
30%
(01:44)
wrong
based on 387
sessions
History
Date
Time
Result
Not Attempted Yet
Of the students at a certain school, 40 took French, 30 took Latin, and 20 took Spanish. How many students at the school took only two of the three languages?
(1) 5 students at the school took all three of the languages.
(2) 52 students at the took took at least one of the languages.
(1) 5 students at the school took all three of the languages.
(2) 52 students at the took took at least one of the languages.
25 Mar 2024, 21:04
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jawnjon
Given: Of the students at a certain school, 40 took French, 30 took Latin, and 20 took Spanish.
Asked: How many students at the school took only two of the three languages?
All = 40 + 30 + 20 - Exactly 2 - 2*All 3 + none
(1) 5 students at the school took all three of the languages.
All = 40 + 30 + 20 - Exactly 2 - 2*5 + none
At least one = 40 + 30 + 20 - Exactly 2 - 2*5
Since number of all students opting for all languages and number of students opting for none of the languages are unknown
NOT SUFFICIENT
(2) 52 students at the school took at least one of the languages.At least one = 40 + 30 + 20 - Exactly 2 - 2*all 3 = 52
Since number of all students opting for all languages is unknown
NOT SUFFICIENT
(1) 5 students at the school took all three of the languages.
(2) 52 students at the school took at least one of the languages.
At least one = 40 + 30 + 20 - Exactly 2 - 2*5 = 52
Number of student opting for Exactly 2 languages = 40 + 30 + 20 - 52 - 10 = 28
SUFFICIENT
IMO C
Given: Of the students at a certain school, 40 took French, 30 took Latin, and 20 took Spanish.
Asked: How many students at the school took only two of the three languages?
All = 40 + 30 + 20 - Exactly 2 - 2*All 3 + none
(1) 5 students at the school took all three of the languages.
All = 40 + 30 + 20 - Exactly 2 - 2*5 + none
At least one = 40 + 30 + 20 - Exactly 2 - 2*5
Since number of all students opting for all languages and number of students opting for none of the languages are unknown
NOT SUFFICIENT
(2) 52 students at the school took at least one of the languages.At least one = 40 + 30 + 20 - Exactly 2 - 2*all 3 = 52
Since number of all students opting for all languages is unknown
NOT SUFFICIENT
(1) 5 students at the school took all three of the languages.
(2) 52 students at the school took at least one of the languages.
At least one = 40 + 30 + 20 - Exactly 2 - 2*5 = 52
Number of student opting for Exactly 2 languages = 40 + 30 + 20 - 52 - 10 = 28
SUFFICIENT
IMO C
General Discussion
12 May 2024, 15:22
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Total - neither language = total of set 1 + total of set2 + total of set 3 - only 2 - 2* all 3
At least one of the three = 40 + 30 + 20 - only 2 - 2*All3
Statement 1 gives the info about all 3 i.e 5
Statement 2 gives the info about at least one of the three i.e 52 ( total no of students in the school minus students learning no language )
C is the answer.
At least one of the three = 40 + 30 + 20 - only 2 - 2*All3
Statement 1 gives the info about all 3 i.e 5
Statement 2 gives the info about at least one of the three i.e 52 ( total no of students in the school minus students learning no language )
C is the answer.
