Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of...

[BTGmoderatorLU]

Source: GMAT Prep

Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teachers 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.

The OA is A

[deloitte247]

Men + women = 1400
Let men = m, and women = w
Total teachers considering engagement = 42% of 1400
Let men considering engagement = x
Let women considering engagement = y
42% of 1400 = x + y
How many of the college teachers surveyed were women? i.e find the value of w

Statement 1 => In the survey 36% of men and 50% of women said that they consider engaging in research activity an essential goal
x = 36% of m = 0.36 m and
y = 50% of w = 0.5 w
m + w = 1400 and m = 1400 - w_____eqn1
42% of 1400 = 0.36m + 0.5w
588 = 0.36m + 0.5w______eqn 2
Substituting m = 1400 - w in equation 2
0.36(1400 - w) + 0.5w = 588
504 - 0.36w + 0.5w = 588
$$\frac{0.14w}{0.14}=\frac{84}{0.14}$$
w = 600
Statement 1 is SUFFICIENT

Statement 2 => In the survey, 288 men said that they consider engaging in research activity an essential goal
42% of 1400 = x + y where x = 288
y = 588 - 288 = 300 but this does not give the value of w, so statement 2 is NOT SUFFICIENT
Since statement 1 alone is SUFFICIENT

Answer = A