Grade Fraction of the population A 0.1 B 0.4 C 0.3 D 0.2
What is the least possible population of the class?
Determining Least Class Population from Grade Fractions
The problem asks for the minimum possible number of students in a class, given the fraction of students who received each grade (A, B, C, D).
The grade distribution is provided as:
| Grade | Fraction |
| A | 0.1 |
| B | 0.4 |
| C | 0.3 |
| D | 0.2 |
Analyzing Grade Fractions
The fractions represent the proportion of the total class population. To find the least possible population, we need to express these fractions in their simplest forms and find the Least Common Multiple (LCM) of their denominators.
- Grade A: $0.1 = \frac{1}{10}$
- Grade B: $0.4 = \frac{4}{10} = \frac{2}{5}$
- Grade C: $0.3 = \frac{3}{10}$
- Grade D: $0.2 = \frac{2}{10} = \frac{1}{5}$
Calculating the Least Common Multiple (LCM)
The denominators of the simplified fractions are 10 and 5.
The least common multiple (LCM) of 10 and 5 is the smallest positive integer that is divisible by both 10 and 5.
- Multiples of 10: 10, 20, 30, ...
- Multiples of 5: 5, 10, 15, 20, ...
The LCM(10, 5) is 10.
Finding the Least Possible Population
The least possible population of the class must be a number that allows for these exact fractional distributions. This number is the LCM of the denominators of the fractions.
Therefore, the least possible population of the class is 10.
This corresponds to Option D.
Important Questions from Percentage (Notes)
- 20% of a number is more than 20% of 620 by 210. The number is:
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