ktrout2020 wrote:Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?
(1) Among the Springfield children, 20 percent of the girls and more than 10 percent of the boys suffered adverse effects after taking the vaccination.
(2) Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.
Target question: Did at least 15 percent of the children in Springfield suffer adverse effects after taking a certain vaccination?
Statement 1: Among the Springfield children, 20% of the girls and more than 10% of the boys suffered adverse effects after taking the vaccination.
This question tests an important (and often-tested) GMAT concept -
weighted averages.
Let's say that
12% of the boys suffered adverse effects.
There are three possible scenarios to consider:
a) IF there were an EQUAL number of boys and girls, then the percentage of
all children who suffered adverse effects would equal the
average of
12% of
20%. So, the percentage of
all children who suffered adverse effects would equal (
20% +
12% )/2 =
16%
b) IF there were an MORE girls than boys, then the percentage of
all children who suffered adverse effects would be closer to
20% than to
12%
c) IF there were an MORE boys than girls, then the percentage of
all children who suffered adverse effects would be closer to
12% than to
20%
Now consider the following CONFLICTING cases
Case a: 20% of the girls suffered adverse effects, and 20% of the boys suffered adverse effects. If there are 2 girls and 2 boys, then
20% of all children suffered adverse effects.
Case b: 20% of the girls suffered adverse effects, and 11% of the boys suffered adverse effects. If there are 2 girls and 1000 boys, then
the percentage of all children who suffered adverse effects will be very very close to 11%, since the boys have the bigger influence on the total percentage
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Among the Springfield children, 20 percent of the boys and more than 15 percent of the girls suffered adverse effects after taking that vaccination.
Since both groups (boys and girls) are such that EACH suffered more than 15% , then
the COMBINED population is certain to have an adverse rate that's greater than 15%
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
