Let me try and explain this with the help of a diagram,

Option 1:

Research No-Research Total

Men .36x 0.64x x


Women .50y .50y y

588 812 1400


> 42 % of the total wish to engage in research = 588; calculate the non-research section = 812.
> Let total of men be x and women be y.
> 36% of the men consider engaging in research = .36x
> 50% of the women consider engaging in research = 0.50y.

As you can see, you can solve for x and y from the above (considering each column one at a time).

Option 2: Use the same table above and remove the values for option 1 and you will see that you are only able to replace the combination of (Men + Research) with 288 and hence compute (Women + Research) as 300, but are unable to find out the total number of women as you don't have sufficient information.

Hence, A should be the correct answer.

Of the 1400 teachers surveyed 42% said that they considered engaging in research an essential goal. How many of the teachers surveyed were women?

(1) In the survey 36% of the men and 50% of the women said that they considered engaging in research an essential goal.
(2) In the survey 288 men said that they considered engaging in research an essential goal.

To deal with DS questions efficiently:

-- Translate the words into math in order to see what you know
-- Before examining the 2 statements, try to determine what you need in order to answer the question
-- Remember that you need as many equations as you have variables in order to solve

In the problem above:

What do we know?
Let M=men and W=women.
M+W = 1400
.42*1400 consider research an essential goal

What do we want?
The value of W.

What do we need?
Since we have 2 variables and 1 equation, we need a 2nd equation.

Statement 1:
.36M + .5W = .42*1400
Statement 1 gives us a 2nd equation.
SUFFICIENT.

Statement 2:
288 men consider research an essential goal
Number of women who consider research an essential goal = .42*1400 - 288
No info about how many women didn't consider research an essential goal.
So no way to determine the total number of women.
INSUFFICIENT.

The correct answer is A.