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