On a field trip, 3/4 of the students in a class attended, and exactly 27 students attended. How many students are in the class?
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Answer & Explanation
Correct answer
C
If 3/4 of the class equals 27, then one quarter of the class is 27 ÷ 3 = 9 students. The full class is four quarters: 9 × 4 = 36, choice (C). Equivalently, divide 27 by 3/4, which means 27 × 4/3 = 36.
The key insight is recognizing that 27 is already the three quarters, not the whole, so you scale 27 up to the full class rather than taking a fraction of it.
(A) 20 is what you get if you take 3/4 of 27 (3/4 × 27 ≈ 20.25), treating 27 as the whole class instead of as the three quarters. (B) 30 comes from dividing 27 into 9 parts instead of 3 to find a quarter, getting 3, then adding it to 27. (D) 40 comes from inverting 4/3 to 3/2 when dividing by 3/4, giving 27 × 3/2 = 40.5. (E) 108 multiplies 27 by 4 without first dividing by 3, so it scales the full three quarters by four instead of scaling a single quarter.