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20 Sep 2019, 00:39
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
91% (01:20) correct
9%
(01:35)
wrong
based on 55
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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
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
20 Sep 2019, 01:19
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If just 33 students like books.
So,50-33=17
50= 57-x+17
x=24
If all students like at least one of the books.
50-50=0
50=57-x+0
x=7
Hence, option B
Posted from my mobile device
So,50-33=17
50= 57-x+17
x=24
If all students like at least one of the books.
50-50=0
50=57-x+0
x=7
Hence, option B
Posted from my mobile device
MathRevolution
Let's say we have a set M and set H. We know N is the overlap in the set.
We know for a set, M ⋃ H = M + H - (M ⋂ H)
and M ⋃ H = 50, M = 33, H = 24
So M ⋂ H = 7;
For the higher range, we need that maximum num of students like both. But that cannot exceed minim between the no. of students that like
H and that like M. which means :
maximum possible value of N = max(0, min(n(H), n(M))) = 24.
So the range is between 7 and 24.
That was a long explanation which helps in finding both the ends of the range. If you just want to solve the question, then you see that either max or min values, once found, matches in only 1 answer. So you don't have to worry about finding the other value.
