Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?
(1) In the survey 36% of men and 50% of women said that they consider engaging in research activity an essential goal.
(2) In the survey 288 men said that they consider engaging in research activity an essential goal.
OA A
Source: GMAT Prep
Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the
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Let \(m =\) men and \(w =\) womenBTGmoderatorDC wrote: ↑Sat May 01, 2021 3:48 pmOf the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?
(1) In the survey 36% of men and 50% of women said that they consider engaging in research activity an essential goal.
(2) In the survey 288 men said that they consider engaging in research activity an essential goal.
OA A
Source: GMAT Prep
\begin{cases}
m + w = 1400 \\
36m + 50w = 58800
\end{cases}
Since we have \(2\) equations for \(2\) unknowns we can solve for either of the values hence \(1\) is sufficient.
For \(2,\) it merely mentions the total number of men and with the given data number of women cannot be found, hence, insufficient.
Therefore, A
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Target question: How many women?BTGmoderatorDC wrote: ↑Sat May 01, 2021 3:48 pmOf the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?
(1) In the survey 36% of men and 50% of women said that they consider engaging in research activity an essential goal.
(2) In the survey 288 men said that they consider engaging in research activity an essential goal.
OA A
Source: GMAT Prep
Let W = # of women
Let M = # of men
Given: W + M = 1400
Statement 1: In the survey 36% of the men and 50% of the women said that they considered engaging in research an essential goal.
0.36M + 0.50W = # of teachers who consider research essential.
Well, we're already told that 42% of all 1400 teachers consider research essential.
So, 0.36M + 0.50W = (0.42)(1400)
So we have W + M = 1400 and 0.36M + 0.50W = (0.42)(1400)
Since we could solve this system for M and W, we can definitely answer the target question with certainty.
This means that statement 1 is SUFFICIENT
Statement 2: In the survey, 288 men said they considered engaging in research an essential goal.
We don't know the number of men altogether, so we don't know the percentage of men who consider research essential. Plus, we don't know anything about the women.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent