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15%
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Of the students in a certain class, 40 learn Spanish, 30 learn French, and 20 learn Italian. If each of her students learn at least one of the languages, how many students learn exactly two of the languages?
(1) There are 60 students in the class.
(2) 10 of the students learn all of the three languages.
(1) There are 60 students in the class.
(2) 10 of the students learn all of the three languages.
thanhtra01011
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Schools: Yale '27 (D) Fuqua '27 (A$$) Tuck '27 (A) Johnson '27 (A$$) Anderson '27 (A$$) Goizueta '27 (A$$$) Ross '27 (A$)
GMAT Focus 1: 665 Q88 V83 DI78
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30 Apr 2024, 03:19
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Given: 40 took S, 30 took F, and 20 took I. All took at least 1
All = 40 + 30 + 20 - Exactly 2 - 2*All 3 + 0
(1) There are 60 students in the class.
60 = 40 + 30 + 20 - Exactly 2 - 2*All 3 + 0
NOT SUFFICIENT
(2) 10 of the students learn all of the three languages.
All = 40 + 30 + 20 - Exactly 2 - 2*10 + 0
NOT SUFFICIENT
Combining (1) (2)
60 = 40 + 30 + 20 - Exactly 2 - 2*10 + 0
=> Exactly 2 = 10
SUFFICIENT
IMO C
All = 40 + 30 + 20 - Exactly 2 - 2*All 3 + 0
(1) There are 60 students in the class.
60 = 40 + 30 + 20 - Exactly 2 - 2*All 3 + 0
NOT SUFFICIENT
(2) 10 of the students learn all of the three languages.
All = 40 + 30 + 20 - Exactly 2 - 2*10 + 0
NOT SUFFICIENT
Combining (1) (2)
60 = 40 + 30 + 20 - Exactly 2 - 2*10 + 0
=> Exactly 2 = 10
SUFFICIENT
IMO C
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