Data Sufficiency

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


OA: A

I understand in theory why the answer is what it is, but if someone could show me proof of it (even though I know solving in DS is unnecessary), I would appreciate it!

Thanks!

Set up a grid, which makes your life easier.

Two sets: Research, male

Research and not-research are complementary. Use this to name two columns or two rows.
male and female are complementary. Use this to name two rows or two colums.

Two equations:

x=men
y=women
total=1400
research essential = 1400 * .42 = 588


Eq 1 => x + y = 1400

and

Eq 2 => .36x + .5y = 588

Solve for y

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


OA: A

I understand in theory why the answer is what it is, but if someone could show me proof of it (even though I know solving in DS is unnecessary), I would appreciate it!

Thanks!

It's probably a bit too late to answer this question, (seeing as it was posted in 2008!) but I'll attempt an answer anyway for the sake of those who will see this later. I also got the question wrong in my GMAT prep test and even thought the answer was [C] . Imagine my surprise when I realized it was not. I checked the forums too and thanks to Kalvin's equations, I was pointed in the right direction.

I actually worked out the .36x + .5y and got a round figure number (I don't want to spoil the fun for you, ) So I went back to the question and wondered what was wrong with Statement 2. I mean, from the question we know that 588 teachers said they considered research essential (588 is 42% of 1400) and from S2, 288 were men. So 588-288= 300. 300 women said they considered research essential. Sufficient, right? WRONG!!!

This is where the testmakers reveal themselves to be geniuses. They know you're probably pressed for time and under pressure and will therefore skim over the question. But the real kernel of the question is hidden in plain sight. The question asks- how many women were surveyed? Not how many said they considered research essential! From S2, we know that 300 women considered research essential, but we don't know how many women were surveyed IN TOTAL i.e. those who said yes + those who said no + the maybes. S2 is insufficient because it gives us the number of men who said yes, not the TOTAL number of men. S1 on the other hand helps us to find the number of total women (and men) surveyed but hides them in percentages. Work out the percentages with 1400 against 588 and you have your answer. So indeed the answer is A. I hope this helps someone!!! I would love to know it did.
Thanks.

For those who are still clueless, the total number of women surveyed is 600