Problem Solving

A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain GMAT = (number of geese of that GMAT migrating) / (total number of geese of that GMAT)]

A. 1/4
B. 7/12
C. 2/3
D. 7/8
E. 8/7

Answer: B

Source: GMAT Prep

Total male = 30%
Female = 100 - 30 = 70%
From total geese migrated, 20% were made; female = 100 - 20 = 80%
Migration rate for geese of a certain GMAT = (no. of geese of that GMAT migrating) / (total number of geese of that GMAT)
$$Migration\ rate\ for\ male=\frac{0.2}{0.3}\ \frac{\left(from\ 20\%\right)}{\left(from\ 30\%\right)}$$
$$Migration\ rate\ for\ female=\frac{0.8}{0.7}\ \frac{\left(from\ 80\%\right)}{\left(from\ 70\%\right)}$$
$$Ratio\ of\ migration\ rate=\frac{\frac{0.2}{0.3}}{\frac{0.8}{0.7}}$$
$$=\frac{0.2}{0.3}\cdot\frac{0.7}{0.8}$$
$$=\frac{0.14}{0.24}=\frac{0.07\cdot100}{0.12\cdot100}=\frac{7}{12}$$

Answer = option B