Among 50 students 33 students like Math and 24 students like

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Sep 19, 2019 11:21 pm

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[GMAT math practice question]

Among 50 students 33 students like Math and 24 students like History. N students like both Math and History. What is the range of N?

A. between 8 and 20
B. between 7 and 24
C. between 12 and 32
D. between 10 and 30
E. between 9 and 25

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Source: Beat The GMAT — Problem Solving | Thu Sep 19, 2019 11:21 pm

Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Sep 22, 2019 5:39 pm

=>

Let n(X) denote the number of elements of a set X.
Since we have 33 ≤ n(A ∪ B) ≤ 50 and n(A ∪ B)=n(A)+n(B)-n(A ∩ B), we have 33 ≤ n(A)+n(B)-n(A ∩ B) ≤ 55 and 33 ≤ 33+24- n(A ∩ B) ≤ 55
Then, we have 7 ≤ n(A ∩ B) ≤ 24.

Therefore, B is the answer.
Answer: B

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