Of the 1400 teachers surveyed 42% said that they considered

[Luci]

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.

Correct answer is A.

I always have problems with this tipe of DS questions. I thought C was the answer because if we now 288 is 36% of the men, then we know the proportion of men and women of the 1400, but I dont understand how with 1 alone can we solve it.

We know that 42% out of 1400 is 588 teachers who considered engaging in research an essential goal. Statemen 1 states that 36% of men and 50% of women completed this 588, but since we dont know the proportion...

Any help?

Thanks

[StaceyKoprince]

Ah, but we do know the proportion... that's the key. :) This is essentially a weighted average question, and these have been popping up more lately, so make sure you know how to do these.

1400 * 42% = # who consider research an important goal. 42% represents the (weighted) number of men and women in this category.

If 36% of men are in this category and 50% of women are in this category, that's enough to tell me the proportion and, therefore, how many women (and men) there are.

(the number of M in this category + number of W in this category ) / total number of men and women = 1400 * 42%

M = total # of men, W = total # of women, and M+W = 1400

0.36M = number of men in the category
0.5W = number of women in the category
.36M + .5W = 1400*42%
couple this with M+W = 1400, and I can solve for M and W.

Note that if you get yourself to the point where you really understand how weighted averages work, you won't even have to do the above calculations - you'll just know that knowing the information given in the problem combined with the info given in statement 1 will be enough to do that calculation.

[Luci]

Great explanation Stacey, it looks easy now. Hopefully I wont fail this kind of problem anymore.

Thanks