Women College teachers- CAT 1

[riks100]

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

The ans for this is A
Can you please explain why it is not C?

[abovethehead]

stem: 42/100 x 1400 said that they considered engaging..., so 588 are considered engaging, 812 are not considered engaging...

2) of the 588, 288 are men, so 300 are women are engaging -- but how many women are NOT considered engaging...?
INSUFFICIENT

harder of the 2 statements:

1) 36% of Men and 50% of Women are considered engaging...so 36/100 M + 50/100 W = 588 and M + W = 1400

2 distinct linear equations, 2 variables
SUFFICIENT

answer is A

[RonPurewal]

stem: 42/100 x 1400 said that they considered engaging..., so 588 are considered engaging, 812 are not considered engaging...

2) of the 588, 288 are men, so 300 are women are engaging -- but how many women are NOT considered engaging...?
INSUFFICIENT

harder of the 2 statements:

1) 36% of Men and 50% of Women are considered engaging...so 36/100 M + 50/100 W = 588 and M + W = 1400

2 distinct linear equations, 2 variables
SUFFICIENT

answer is A

this is good. remember that you don't have to actually solve a system, if you know that it can be solved for a unique solution.

note that this is a WEIGHTED AVERAGES problem.
on weighted averages problems, if you know any 2 of the following 3, then you can find the third one:
1. the ratio of 'weights' of the different quantities
2. the values of the quantities
3. the weighted average

in this problem, we have the values of the quantities (36 and 50), as well as the weighted average (42). that's enough information to find the ratio of the 'weights' (which happens to be 4:3 m:f, although you don't particularly care because it's data sufficiency).
because you have a total for everybody (1400), that ratio is enough to give you a hard number for the # of women.
sufficient.

--

if you know the relationships posited above, you can get through weighted averages on data sufficiency very quickly - although it's still helpful to know the algebraic method so you can break it out on problem solving.

[sudaif]

this question can also be easily solved using a double set matrix. statement 1 gives you two linear equations with two variables that can be simultaneously solved for unique solutions for each variable. just a thought...
Wtd average is such a dominant topic on GMAT!

[RonPurewal]

this question can also be easily solved using a double set matrix. statement 1 gives you two linear equations with two variables that can be simultaneously solved for unique solutions for each variable. just a thought...
Wtd average is such a dominant topic on GMAT!

yep -- correct.

by the way, if you're going to make posts like this one, please give the specifics
i.e., don't just state that "there are two linear equations" -- give the equations! if you don't, then there is very little point in posting this.

--

i'm assuming that you're talking about the following equations:
let m = # of male teachers, w = # of female teachers
then
m + w = 1400
0.36m + 0.50w = 0.42(1400)

--

by the way, if we change statement (1) to say
In the survey 42% of the men and 42% of the women said that they considered engaging in research an essential goal
... then it's now insufficient.
make sure you know why.

[tsiria]

this question can also be easily solved using a double set matrix. statement 1 gives you two linear equations with two variables that can be simultaneously solved for unique solutions for each variable. just a thought...
Wtd average is such a dominant topic on GMAT!

yep -- correct.

[color=#FF0000]by the way, if you're going to make posts like this one, please give the specifics
i.e., don't just state that "there are two linear equations" -- give the equations! if you don't, then there is very little point in posting this.

--[/color]

i'm assuming that you're talking about the following equations:
let m = # of male teachers, w = # of female teachers
then
m + w = 1400
0.36m + 0.50w = 0.42(1400)

--

by the way, if we change statement (1) to say
In the survey [color=#408000]42% of the men and 42% of the women said that they considered engaging in research an essential goal
... then it's now insufficient.
make sure you know why.

[/color]

Is it because it just repeats information already given in the question stem? .42M+.42W = .42(1400) --->
.42(M+W) =.42(1400)
but M+W = 1400 ---> .42(1400)=.42(1400)
Does not give us any useful new information.

[RonPurewal]

Is it because it just repeats information already given in the question stem? .42M+.42W = .42(1400) --->
.42(M+W) =.42(1400)
but M+W = 1400 ---> .42(1400)=.42(1400)
Does not give us any useful new information.

no ... that would definitely give you new information. the fact that 42% is the individual percentage of both men and women is much, much more specific than the fact that 42% is a composite weighted average.
(you'll be able to think about this more intuitively if you think with "half" instead of "42%". i.e., knowing that half of all men *and* half of all women support something is much more specific information than just knowing that half of everyone supports it.)

the reason why 42% and 42% wouldn't help is that you would no longer be able to determine the "weights" in the weighted average. i.e., if 42% of one population and 42% of another population support something, then the weighted average will *always* be 42%, regardless of the relative sizes of the two populations.
on the other hand, a weighted average of two different figures will vary according to the relative population/sample sizes. for instance, a weighted average of 40% men / 50% women can only be 42% of the ratio of men to women is exactly four to one.

[ghong14]

Can someone explain why b is insufficient? If we know that there are 288 men shouldn't the number of woman be 1400(42/100)-288. After all there are only men and woman???

[RonPurewal]

Can someone explain why b is insufficient? If we know that there are 288 men shouldn't the number of woman be 1400(42/100)-288. After all there are only men and woman???

That would only work if 42% of men -- separately -- and also 42% of women -- separately -- had this goal.

The point of the problem is that those individual percentages aren't 42%, although the overall percentage is.

[mrwells2]

stem: 42/100 x 1400 said that they considered engaging..., so 588 are considered engaging, 812 are not considered engaging...

2) of the 588, 288 are men, so 300 are women are engaging -- but how many women are NOT considered engaging...?
INSUFFICIENT

harder of the 2 statements:

1) 36% of Men and 50% of Women are considered engaging...so 36/100 M + 50/100 W = 588 and M + W = 1400

2 distinct linear equations, 2 variables
SUFFICIENT

answer is A

this is good. remember that you don't have to actually solve a system, if you know that it can be solved for a unique solution.

note that this is a WEIGHTED AVERAGES problem.
on weighted averages problems, if you know any 2 of the following 3, then you can find the third one:
1. the ratio of 'weights' of the different quantities
2. the values of the quantities
3. the weighted average

in this problem, we have the values of the quantities (36 and 50), as well as the weighted average (42). that's enough information to find the ratio of the 'weights' (which happens to be 4:3 m:f, although you don't particularly care because it's data sufficiency).
because you have a total for everybody (1400), that ratio is enough to give you a hard number for the # of women.
sufficient.

--

if you know the relationships posited above, you can get through weighted averages on data sufficiency very quickly - although it's still helpful to know the algebraic method so you can break it out on problem solving.

Hi Ron, I know this is an old bump but can you clarify something for me.

In your 3 rules for a weighted averages problem, do you also need to know the TOTAL that the ratios, values, or weighted average is referring to in order for these rules to work?

Thanks in advance. If you could also direct me to any additional Weighted Average topics, or your own explanations, I'd appreciate it.

[RonPurewal]

the takeaway is, essentially, that a weighted average is just another way to express a ratio.

this kind af abstract language is not my thing, so let's talk specific examples.
a woman has 2 X-chromosomes; a man has 1 X-chromosome.

the following are all identical, for a group comprising men and women:
• the average number of X-chromosomes per person is 1.4
• the ratio of men to women is 3:2
• men make up %60 of the group
• women are 2/5 of the group
etc.
the weighted average is the first of these. provided you have the information above (1 x-chromosome per man, 2 per woman), it's exactly equivalent to the others.

[RonPurewal]

regarding your question about totals, you should be able to figure out the idea from the last post.

all of those things are ratios. none of them depends on the actual numbers of men and women. (in fact, "doesn't require actual numbers" is the whole point of ratios in the first place; if that weren't true, there would be no reason for ratios to exist.)

so, you won't need a total, unless the goal of the problem is to find an actual number.
in that case, you'll need an actual number to find other actual numbers. not necessarily a total, but a specific number.

e.g., if the question is "how many women are in the group?", then none of the equivalent things above will give a number.
however, if any of those statements is combined with an actual number (total, or # men, or whatever), then you'll have the number of women.

[mrwells2]

regarding your question about totals, you should be able to figure out the idea from the last post.

all of those things are ratios. none of them depends on the actual numbers of men and women. (in fact, "doesn't require actual numbers" is the whole point of ratios in the first place; if that weren't true, there would be no reason for ratios to exist.)

so, you won't need a total, unless the goal of the problem is to find an actual number.
in that case, you'll need an actual number to find other actual numbers. not necessarily a total, but a specific number.

e.g., if the question is "how many women are in the group?", then none of the equivalent things above will give a number.
however, if any of those statements is combined with an actual number (total, or # men, or whatever), then you'll have the number of women.

Thanks for the clarification. I understand it now.

Ratio + Sum = exact total
Ex: Ratio of men to women is 3:1. There is a total of 8 people in the room. Therefore there are 6 men and 2 women. .
Ratio + 1 total = exact total
Ex: ratio of men to women is 3:1. There are 2 women in the room. How many men? There are 6 men.

Thanks again, and I hope you're not on EST right now. 5:45am is the crack of dawn.

[jnelson0612]

Glad that everything makes sense now! :-)

[RonPurewal]

if you have any other questions, please let us know. thanks.

Thanks again, and I hope you're not on EST right now. 5:45am is the crack of dawn.

"early" and "late" are determined by when a person rises, not by when the sun rises.