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06 Feb 2025, 01:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (01:57) correct
45%
(02:12)
wrong
based on 155
sessions
History
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Time
Result
Not Attempted Yet
There are a total of 200 students. Each student must take at least one of the three languages: German, French, or Spanish. Among them, 100 students take German, and none of the students who take French also take Spanish. The goal is to determine how many students take exactly two of the three languages.
(1) 80 students take only German.
(2) 120 students take either French or Spanish.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) 80 students take only German.
(2) 120 students take either French or Spanish.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
06 Feb 2025, 02:55
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\(G, F \) & \( S\) are the three languages.
Since French takers didn't take Spanish, students took only \(GS\) & \(GF\) as multiple languages and none of them take all three languages
Statement 1: 80 students take only German.
Out of 100, 80 took only \(G\). Remaining 20 either took \(GF\) or \(GS\)
Sufficient
Statement 2: 120 students take either French or Spanish.
\(F+S=120\)
\(200=G+F+S-(GS+GF)= 100+120-(GS+GF) \)
\({GS+GF}=20\)
Sufficient
Answer: D
Since French takers didn't take Spanish, students took only \(GS\) & \(GF\) as multiple languages and none of them take all three languages
Statement 1: 80 students take only German.
Out of 100, 80 took only \(G\). Remaining 20 either took \(GF\) or \(GS\)
Sufficient
Statement 2: 120 students take either French or Spanish.
\(F+S=120\)
\(200=G+F+S-(GS+GF)= 100+120-(GS+GF) \)
\({GS+GF}=20\)
Sufficient
Answer: D
06 Feb 2025, 03:20
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Given,
Total = 200
None = 0
All 3 = 0, since none of the students who take French also take Spanish
G = 100
SF = 0
Statement 1:
Only G = 80
G - Only G = Exactly 2 language (GS+GF, as SF = 0)
Exactly 2 language = 100-80 = 20
B,C E is out
Statement 2:
T = G + S + F - B
200 = 100 +120 - B
B = 20
Answer is D
Total = 200
None = 0
All 3 = 0, since none of the students who take French also take Spanish
G = 100
SF = 0
Statement 1:
Only G = 80
G - Only G = Exactly 2 language (GS+GF, as SF = 0)
Exactly 2 language = 100-80 = 20
B,C E is out
Statement 2:
T = G + S + F - B
200 = 100 +120 - B
B = 20
Answer is D
Bunuel
