In a college, 1/5 of the girls and 1/8 of the boys participated in a social camp. What fraction of the total students took part? (Assume only girls and boys; evaluate if the data suffice.)

Introduction / Context:
Data sufficiency questions check whether provided ratios uniquely determine a required overall fraction. Here, different participation rates are given for girls and boys, and we are asked for the fraction of the total student body that participated. Without the composition of the population, the overall fraction may vary.

Given Data / Assumptions:

• Girls participation rate: 1/5 of girls.
• Boys participation rate: 1/8 of boys.
• Total students = girls + boys; only these two categories.
• We are not given the number or ratio of girls to boys.

Concept / Approach:
Let G be the number of girls and B be the number of boys. The total participants equal G/5 + B/8. The total students equal G + B. The requested fraction is (G/5 + B/8) / (G + B). Without a fixed ratio G:B, this value changes with G and B, so the answer cannot be uniquely determined from the given information alone.

Step-by-Step Solution:
Participants = G/5 + B/8.Total = G + B.Required fraction = (G/5 + B/8) / (G + B).Pick two different mixes to see variation:Example 1: Let G = 80, B = 80 → participants = 16 + 10 = 26 → fraction = 26/160 = 13/80.Example 2: Let G = 40, B = 120 → participants = 8 + 15 = 23 → fraction = 23/160 = 23/160.Different fractions arise, so no single fraction is determined.

Verification / Alternative check:
Algebraically, (G/5 + B/8)/(G + B) cannot be simplified to a constant without knowing G:B. Hence multiple valid outcomes exist.

Why Other Options Are Wrong:

• 13/40 / 13/80 / 2/13: Each may occur only for specific G:B values; none is universally correct.
• Cannot be determined: Equivalent in meaning to “Data inadequate”; both reflect the same conclusion (we key to the listed correct option).

Common Pitfalls:
Assuming equal numbers of girls and boys without being told; averaging the rates 1/5 and 1/8 directly, which is invalid for different group sizes.

Final Answer:
Data inadequate