In a classroom the number of boys is three times the number of girls. Which of the following numbers does not represent the total number of students in the classroom?

## Concept & Logic This problem relies on basic ratios and divisibility rules. Since the number of human beings (students) must be an integer, the total number of students must be a multiple of the sum of the ratio units. $$ Total\ Units = Ratio_1 + Ratio_2 $$ $$ Total\ Population = Integer \times Total\ Units $$ ## Step-by-Step Solution * **Given:** Number of boys = $3 \times$ Number of girls. * **Deduction:** Let the number of girls be $x$. Then, the number of boys is $3x$. * **Calculation:** The total number of students in the classroom is the sum of boys and girls. Total = $x + 3x = 4x$. * **Conclusion:** Since $x$ (number of girls) must be a whole number, the total number of students ($4x$) must be a perfect multiple of 4. * **Evaluation:** Check the given options against divisibility by 4: (a) $40 = 4 \times 10$ (Valid) (b) $42 = 4 \times 10.5$ (Invalid, results in a fractional person) (c) $44 = 4 \times 11$ (Valid) (d) $48 = 4 \times 12$ (Valid) * **Conclusion:** 42 cannot represent the total number of students. ## Exam Strategy & Shortcut Simply identify the ratio: Boys : Girls = $3 : 1$. Sum of ratio parts = $3 + 1 = 4$. The correct answer must be the option that is **not** divisible by 4. Looking at the options: 40, 44, and 48 are clearly multiples of 4. 42 is not. Done. ## Common Pitfall Overthinking the problem or trying to set up complex algebraic systems. Recognizing that populations must be discrete integers immediately unlocks the "divisibility by ratio sum" trick. ## Final Answer Therefore, the correct answer is **42**.