msch14 wrote:Of 1400 college teachers surveyed, 42% said they considered research essential. How many teachers surveyed were women?
a. In survey 36% of men and 50% of women said they considered research essential
b. 288 men said they considered research essential
Step 1 of the Kaplan method for data sufficiency: focus on the question stem.
We know that there are 1400 teachers total, and 42% consider research essential. We want to know how many of the 1400 teachers are women.
What do we need? Information about the men/women surveyed.
Step 2: consider each statement by itself.
(1) gives us the % breakdown of answers for men and women.
There are a couple of ways we can show that this is sufficient.
First, algebra:
m + w = 1400 (from the original)
36%(m) + 50%(w) = 42%(1400) (weighted average formula from statement (1) info).
Two equations, two unknowns: we can solve the system... sufficient.
Note: the number of equations vs number of unknowns rule is THE most powerful tool for data sufficiency. The better you understand this rule, the less math you'll have to do to answer DS questions.
Second, critical thinking (which is like algebra without the math!):
we know that the weighted average formula involves an overall average and individual weights. From the stem, we have the overall average. From (1), we have the individual weights. Since we also know the total number of people, we can use the individual weights to calculate how many people are in each group: sufficient.
(2) gives us the number of men who said "essential" in the survey.
Well, this would allow us to calculate the number of women who answered "essential", but tells us nothing at all about the TOTAL number of men and women who were surveyed: insufficient.
(1) is sufficient, (2) is not: choose (A).
