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 sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
A. 1/4
B. 7/12
C. 2/3
D. 7/8
E. 8/7
Answer: B
Source: GMAT Prep
A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during
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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 sex = (no. of geese of that sex migrating) / (total number of geese of that sex)
$$Migration\ rate\ for\ male=\frac{0.2}{0.3}\ \frac{\left(from\ 20\%\right)}{\left(from\ 30\%\right)}$$
$$Migration\ rate\ for\ female=\frac{0.8}{0.7}\ \frac{\left(from\ 80\%\right)}{\left(from\ 70\%\right)}$$
$$Ratio\ of\ migration\ rate=\frac{\frac{0.2}{0.3}}{\frac{0.8}{0.7}}$$
$$=\frac{0.2}{0.3}\cdot\frac{0.7}{0.8}$$
$$=\frac{0.14}{0.24}=\frac{0.07\cdot100}{0.12\cdot100}=\frac{7}{12}$$
Answer = option B
Female = 100  30 = 70%
From total geese migrated, 20% were made; female = 100  20 = 80%
Migration rate for geese of a certain sex = (no. of geese of that sex migrating) / (total number of geese of that sex)
$$Migration\ rate\ for\ male=\frac{0.2}{0.3}\ \frac{\left(from\ 20\%\right)}{\left(from\ 30\%\right)}$$
$$Migration\ rate\ for\ female=\frac{0.8}{0.7}\ \frac{\left(from\ 80\%\right)}{\left(from\ 70\%\right)}$$
$$Ratio\ of\ migration\ rate=\frac{\frac{0.2}{0.3}}{\frac{0.8}{0.7}}$$
$$=\frac{0.2}{0.3}\cdot\frac{0.7}{0.8}$$
$$=\frac{0.14}{0.24}=\frac{0.07\cdot100}{0.12\cdot100}=\frac{7}{12}$$
Answer = option B