At Fractionville Junior High, 40% of the students in seventh grade are in the school band, and there are half as many students in eighth grade as in seventh grade. If 20% of the students in eighth grade are not in the school band, what fraction of the students both in seventh and eighth grade are in the school band?

Incorrect.
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Did you average the two percentages given in the problem to guess the answer? These are percents that relate to different numbers. A GMAT question will never be that simple.

Incorrect.
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Did you assume the same number of students were in both seventh and eighth grades? The number of students in both grades is different: "there are half as many students in eighth grade as in seventh grade."

Incorrect.
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Remember to answer the question asked. You are looking for the fraction of students that are *not* in the school band.

Correct.
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__Plug In__ a good number for the number of students in seventh grade, such as 100. Of the 100 students, 40 are in the school band, and the rest (60) are not. The number of students in eighth grade is half that of seventh grade (i.e., 50 students). Of the students in eighth grade, 20% of the 50 are not in the school band (10) and the rest (40) are. There are $$40+40=80$$ in the school band between the two grades out of 150 students total. Hence, the answer is $$\frac{80}{150} = \frac{8}{15}$$.

Incorrect.
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Did you average the percentages of those in the school band in seventh and eighth grade? Since the number of students in both grades is different, these percents relate to different numbers and cannot be simply averaged.

$$\frac{3}{10}$$

$$\frac{2}{5}$$

$$\frac{7}{15}$$

$$\frac{8}{15}$$

$$\frac{3}{5}$$