This GMAT math practice question is from set theory. Concept tested: Union and intersection of 2 sets. Task: Computing the cardinal number or number of elements in only set A. An easy, GMAT sub 600 level, Set Theory sample question. This set theory question can be solved using formula or using Venn Diagram.
Question 3: In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
Let A be the set of students who have enrolled for English and B be the set of students who have enrolled for German.
Then, (A ∪ B) is the set of students who have enrolled for at least one of the two languages.
Because the students of the class have enrolled for at least one of the two languages, we will not find anyone outside A ∪ B in this class.
Therefore, n(A ∪ B) = number of students in the class
So, n(A ∪ B) = 40
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
i.e., 40 = n(A) + 22 - 12
Or n(A) = 30
n(A) is the number of students who have enrolled for English.
This number is the sum of those who have enrolled for only English and those who have enrolled for both the languages.
What we have to compute the number of students who have enrolled for only English.
n(only English)= n(English) - n(A ∩ B)
= 30 - 12 = 18.
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