Question 1007091: in a class of 30 students, 18 students study history, 16 study geography and 3 study neither subject. how many students undertake geography but not history
Answer by ikleyn(52781)   (Show Source):
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In a class of 30 students, 18 students study history, 16 study geography and 3 study neither subject. How many students undertake geography but not history?
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How many students of the class study at least one of the two subjects, history or geography? 30 - 3 = 27 students.
Now add 18 who study history and 16 who study geography. You will get 18 + 16 = 34.
Why it is more than 27? - It is because some of 18 + 16 study both history and geography.
How many students study both subjects? The answer is: (18 + 16) - 27 = 34 - 27 = 7.
Now we know that 16 students study geography; of them 7 study history.
Thus, it is easy to determine the number of those who study geography only.
It is 16 - 7 = 9.
Answer. The number of students who study only geography is 9.
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