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# Of the 1400 college teachers surveyed, 42% said they considered engagi

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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Thanks for all the help, folks.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Hi Bunuel,
I thought the first statement as 36% of the total men who participated in the survey and similar for women.
The statement itself says In the survey 36% of men and 50% of women said...!!
We cannot calculate the total no. of men and women. participated in the survey from the given information!!
Confused!!

Bunuel wrote:
Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?

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

(1) $$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$. Two unknowns two equations. Sufficient.
(2) From this we can calculate only that $$1400*0.42-288=300$$ women consider engaging in research activity an essential goal. No other info. Not sufficient.

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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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scofield1521

In the above solution

m = total number of men participated in the survey
w = total number of women participated in the survey

Clearly

m+w=1400 -------------- Equation 1

and as per choice a

(0.36 m) = total number of men that considered engaging in research an essential goal
(0.5 w ) = total number of women that considered engaging in research an essential goal

also 0.36 m + 0.5w = 0.42 (1400) ---------------- Equation 2

Hence, A is enough to get the answer.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Hi , has anyone solved this problem using grid method.
I am getting C as the answer by using grid method.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
I (initially) got this wrong using the grid method because I failed to realise that W + M = 1400. I think it just goes to show that it's important to write pretty much everything down while doing a question, so you don't miss anything...
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

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

If we modify the original condition, we can get a '2by2' table, which is one of the most common types of question in GMAT Math
Attachment:

GC DS burmttwinky Of the 1400 college.png [ 3.6 KiB | Viewed 45067 times ]

When looking at the table, we can see that a+b+c+d=1400, a+b=1400*42%.
There are 4 variables and 2 equations, so we need 2 more equations
From condition 1, there are 2 equations (b=0.36(b+d), a=0.5(a+c)), so this is sufficient,
whereas condition 2 only gives one condition (b=288), making this insufficient and the answer becomes (A).
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Bunuel wrote:
Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?

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

(1) $$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$. Two unknowns two equations. Sufficient.
(2) From this we can calculate only that $$1400*0.42-288=300$$ women consider engaging in research activity an essential goal. No other info. Not sufficient.

In such a case, isn't it essential to check the following 2 things regarding statement (1)? :

A. Whether integral solution exists for set of equations
$$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$

B. Whether only a single integral solution exists for the set of equations.

In case the answer to any of the two questions is YES, wouldn't (1) be rendered NOT SUFFICIENT?

PS: When I solved the question, I used the same methodology as yours, but consumed more time because I checked for the two questions mentioned above. Hence, I am interested to know whether you have a definite way of knowing that these 2 additional operations are not required.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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bikographer wrote:
Bunuel wrote:
Of the 1400 college teachers surveyed, 42% said they considered engaging in research an essential goal. How many of the college teacher surveyed were women?

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

(1) $$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$. Two unknowns two equations. Sufficient.
(2) From this we can calculate only that $$1400*0.42-288=300$$ women consider engaging in research activity an essential goal. No other info. Not sufficient.

In such a case, isn't it essential to check the following 2 things regarding statement (1)? :

A. Whether integral solution exists for set of equations
$$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$

B. Whether only a single integral solution exists for the set of equations.

In case the answer to any of the two questions is YES, wouldn't (1) be rendered NOT SUFFICIENT?

PS: When I solved the question, I used the same methodology as yours, but consumed more time because I checked for the two questions mentioned above. Hence, I am interested to know whether you have a definite way of knowing that these 2 additional operations are not required.

Hi,
Quote:
A. Whether integral solution exists for set of equations
$$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$

all the % given are by the Q and nothing is being assumed by us, so if they have given 36% of men and 50% of women are ...., it will always be integer..
Rather you can use this property to home on to some info on m and w...
.36m has to be an integer or 36m/100 is an integer 36m/100 = 9m/25.. this tells us that m has to be a multiple of 25..

there are other Q where you have to check for this but not here as the % are given by the Q..

Quote:
B. Whether only a single integral solution exists for the set of equations.

If you have two distinct linear equation and two variables, ans is YES
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Thanks, chetan2u!

Quote:
A. Whether integral solution exists for set of equations
$$m+w=1400$$ and $$1400*0.42=0.36*m+0.5*w$$

all the % given are by the Q and nothing is being assumed by us, so if they have given 36% of men and 50% of women are ...., it will always be integer..
Rather you can use this property to home on to some info on m and w...
.36m has to be an integer or 36m/100 is an integer 36m/100 = 9m/25.. this tells us that m has to be a multiple of 25..

there are other Q where you have to check for this but not here as the % are given by the Q..

This is something that I wasn't aware of until now. I was under the impression that GMAC could intentionally give us cases where the quantities wouldn't turn out to be integers, just to test whether we would check them or not. I will remember this from now on.

Quote:
B. Whether only a single integral solution exists for the set of equations.
If you have two distinct linear equation and two variables, ans is YES

I now realize how stupid a question 'B' was! :D

Thanks, once again.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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bikographer wrote:
Thanks, chetan2u!

This is something that I wasn't aware of until now. I was under the impression that GMAC could intentionally give us cases where the quantities wouldn't turn out to be integers, just to test whether we would check them or not. I will remember this from now on.

Another point..
If two variables are given without any info, it can be anything -- integers or fraction , + or -
example-- 15x + 12y = 350....
x and y can take any values....

But if it says that 36% are men OR 22% bikes OR 70% cars...
all the things which have to be in integer quantity.. would mean 22% bikes are integer, 70% car is integer etc..
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Thanks everyone for explaining.
So essentially it means that the survey's other group are those who do not consider engaging in resserch an essential goal? with this assumption it becomes a clear A... 250 level.
So this is how we assume it in any question like this?
Kudos awaits replies.

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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Thanks everyone for explaining.
So essentially it means that the survey's other group are those who do not consider engaging in resserch an essential goal? with this assumption it becomes a clear A... 250 level.
So this is how we assume it in any question like this?
Kudos awaits replies.

Posted from my mobile device

Posted from my mobile device
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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Nez wrote:
Thanks everyone for explaining.
So essentially it means that the survey's other group are those who do not consider engaging in resserch an essential goal? with this assumption it becomes a clear A... 250 level.
So this is how we assume it in any question like this?
Kudos awaits replies.

Posted from my mobile device

We are given that 42% of the surveyed said they considered engaging in research an essential goal, thus the remaining 58% of the surveyed did not consider engaging in research an essential goal. This is not an assumption, this is a logical derivation.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Wao.
i thought that there might be other groups like the undecided or indifferent: the Neithers.

Damn GMAT!
Bunuel don't worry, I've knocked your point into my skull.
Thanks a lot.

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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
Let M = men and W = Women

m + w = 1400
36m + 50w = 58800

Since we have 2 equations for 2 unknowns we can solve for either of the values hence 1 is sufficient.
.
For 2 it merely mentions total number of men and with the given data number of women cannot be found hence insufficient.

Answer choice is A
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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

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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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(2)
M + W = 1400

who wants to research = 1400* .42 = (M+W)* .42 = 588
since 1400= M+W so we can replace M+W with 1400

now men who want to do research= 288 = .42M
so .42(M+W )= 588
.42M +.42 W= 588
288 +.42 W = 588
so we can calculate W

so why this is wrong?
Re: Of the 1400 college teachers surveyed, 42% said they considered engagi [#permalink]
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