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Of the 1400 college teachers surveyed, 42% said they considered engagi 28 Apr 2017, 06:08
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vijaisingh2001
(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?
Show more


now men who want to do research= 288 = .42M

How do you get this? 42% of total teachers said that engaging in research is essential. We don't know what percent of men thought so. It is possible that only 30% men considered research essential while 55% women considered research essential. Both together could lead to a number of 42% depending on the ratio of number of men and women. This is just one example. The figure of 42% could be obtained in many different ways.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 06 Jun 2017, 18:48
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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:

\(m+w=1400\) and \(1400*0.42=0.36*m+0.5*w\). Two unknowns two distinct linear equations. Sufficient.

(2) In the survey 288 men said that they consider engaging in research activity an essential goal"

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.

Answer: A.
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Absolutely a brilliant explanation! I had always used the matrix box approach but not anymore '

Thank you Bunuel sir,
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Of the 1400 college teachers surveyed, 42% said they considered engagi 23 Jan 2018, 19:57
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Bunuel, VeritasPrepKarishma

I understand this is a weighted averages problem. But I am having a hard time understanding how we take percentages as the "average" for a group. To me 'averages' are an absolute number (not %). Could you please explain what am I missing here?

BTW, Can you also check if my weighted average solution for this problem is correct?

If we apply the weighted average concept here for choice A:

AvgM = 36%, AvgW = 50%. Total Average (AvgT) = 42%. So since we know all three averages, we can calculate the ratio of the weights using the formula:

Wm/Ww = AvgW - AvgT/AvgT - AvgM. This will give us the ratio of M/W and since we have total of all surveyed, we can find number of women.

I think I am confused as to why we are taking these percentages as Average for that group.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 23 Jan 2018, 21:42
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Bunuel, VeritasPrepKarishma

I understand this is a weighted averages problem. But I am having a hard time understanding how we take percentages as the "average" for a group. To me 'averages' are an absolute number (not %). Could you please explain what am I missing here?

BTW, Can you also check if my weighted average solution for this problem is correct?

If we apply the weighted average concept here for choice A:

AvgM = 36%, AvgW = 50%. Total Average (AvgT) = 42%. So since we know all three averages, we can calculate the ratio of the weights using the formula:

Wm/Ww = AvgW - AvgT/AvgT - AvgM. This will give us the ratio of M/W and since we have total of all surveyed, we can find number of women.

I think I am confused as to why we are taking these percentages as Average for that group.
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Yes, it is and your method is correct.

Percentages are just a way of expressing concentration.
So you have two groups made of two ingredients - "people who consider engaging in research essential" and "people who don't consider it essential"

So we work with the percentage of "people who consider engaging in research essential". It is the same as working with the concentration of one of the ingredients.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 15 Aug 2018, 21:24
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How many of the college teacher surveyed were women? The question does not mention research. The answer should be E.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 16 Aug 2018, 21:15
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s55day
How many of the college teacher surveyed were women? The question does not mention research. The answer should be E.
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Yes, we are looking for the number of women college teachers surveyed (not just those who consider research essential). Stmnt 1 helps you find this number as explained by me (using matrix) on the previous page here:
https://gmatclub.com/forum/of-the-1400- ... l#p1426233

Bunuel has explained it using algebra here: https://gmatclub.com/forum/of-the-1400- ... ml#p707913
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Of the 1400 college teachers surveyed, 42% said they considered engagi 13 Oct 2018, 22:47
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Using Matrix method we can easily solve.

Total survey=1400 teachers out of which 42%(588) find research as essential

Statement 1: out of the surveyed 1400 teachers, 36% are men and 50℅ are women.

Men Women Total
Ess. 36% 50% 588
Not ess. 64%(bal)50%(bal)812(bal)
Total 100% 100% 1400

SUFFICIENT.

Statement 2: only gives information about the men who find research as essential and gives no further information about total women in survey.
INSUFFICIENT.

Therefore, the answer must be A.

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Of the 1400 college teachers surveyed, 42% said they considered engagi 08 May 2019, 12:04
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HiVeritasKarishma

I did figure out that we could use weighted averages for this problem

So we have \(\frac{(50-42)}{(42-36)}= \frac{M}{F}\)

this turn out to be \(\frac{(8)}{(6)}= \frac{M}{F}\)

So can we say in the research group ratio of \(\frac{F}{T}\)= \(\frac{6}{14}\)

Just to solve futher we have 42% 1400= 588

so we have \(\frac{6}{14} *588\)

So we have Females is 252

But my problem is that we are told in the second statement that 288 Men consider Research , so out of 588 we then have 300 Women

1 Contradicts 2. And on Gmat DS two statements never contradict

Can you help me identify my gaps?
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Of the 1400 college teachers surveyed, 42% said they considered engagi 14 May 2019, 06:44
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HiVeritasKarishma

I did figure out that we could use weighted averages for this problem

So we have \(\frac{(50-42)}{(42-36)}= \frac{M}{F}\)

this turn out to be \(\frac{(8)}{(6)}= \frac{M}{F}\)

So can we say in the research group ratio of \(\frac{F}{T}\)= \(\frac{6}{14}\)

Just to solve futher we have 42% 1400= 588

so we have \(\frac{6}{14} *588\)

So we have Females is 252

But my problem is that we are told in the second statement that 288 Men consider Research , so out of 588 we then have 300 Women

1 Contradicts 2. And on Gmat DS two statements never contradict

Can you help me identify my gaps?
Show more

The important thing here is this: What are the weights?

36% of total men and 50% of total women make up 42% of total teachers.

The weights are your total number of men and total number of women.
So your M/F = Total number of men / Total number of women = 8/6

So there are 6 women for every 14 total teachers.

Total number of women = (6/14) * 1400 = 600
Total number of men = (8/14) * 1400 = 800

50% of women consider research essential so 300 women consider research essential
36% of men consider research essential so 36% of 800 = 288 men consider research essential.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 05 Aug 2020, 18:54
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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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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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Aren't we also assuming that everybody answered with either a Yes or a No.
Isn't it possible that some may answered without a Yes/No.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 10 Aug 2020, 22:41
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I think we can use weighted average approach here (42-36)M = (50-42)W
6M=8W M= 4/3 W 4/3W + W = 1400 we can find M and W both. Please let me know if this approach is wrong or will fail in certain scenarios.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 07 Dec 2020, 16:49
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Bunuel
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:

\(m+w=1400\) and \(1400*0.42=0.36*m+0.5*w\). Two unknowns two distinct linear equations. Sufficient.

(2) In the survey 288 men said that they consider engaging in research activity an essential goal"

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.

Answer: A.
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Hi Bunuel - in S1 -- highlighted the bit where I had a question

How do you know (w/o putting pen to paper) the two equations are distinct linear equations.

I thought it's quite possible that the equations are the same if you multiple (m+w = 1400) with some constant, you can get equation 2

Thank you !
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Of the 1400 college teachers surveyed, 42% said they considered engagi 08 Dec 2020, 00:30
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Bunuel
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:

\(m+w=1400\) and \(1400*0.42=0.36*m+0.5*w\). Two unknowns two distinct linear equations. Sufficient.

(2) In the survey 288 men said that they consider engaging in research activity an essential goal"

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.

Answer: A.

Hi Bunuel - in S1 -- highlighted the bit where I had a question

How do you know (w/o putting pen to paper) the two equations are distinct linear equations.

I thought it's quite possible that the equations are the same if you multiple (m+w = 1400) with some constant, you can get equation 2

Thank you !
Show more

We have:
1. \(1400=m+w\)
2. \(1400*0.42=0.36*m+0.5*w\).

If we multiply 1 by 0.42, we get \(1400*0.42=0.42m+0.42w\), not \(1400*0.42=0.36*m+0.5*w\).
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Of the 1400 college teachers surveyed, 42% said they considered engagi 25 Dec 2020, 08:09
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burnttwinky
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.
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Let m = men
Let w = women

m + w = 1400

(1) \(0.36m + 0.5w = 0.42(m + w)\)

\(0.36m + 0.5w = 588\)

\(0.36(1400 - w) + 0.5w = 588\)

\(504 - 0.36w + 0.5w = 588\)

\(504 + 0.14w = 588\)

\(0.14w = 84\)

\(w = 600 \)

SUFFICIENT.

(2) Clearly not sufficient.

Answer is A.
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Of the 1400 college teachers surveyed, 42% said they considered engagi 10 Apr 2021, 21:16
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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.
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Answer: Option A

Video solution by GMATinsight

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Of the 1400 college teachers surveyed, 42% said they considered engagi 27 May 2021, 10:39
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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.
Show more

Target question: How many women?

Let W = # of women
Let M = # of men

Given: W + M = 1400

Statement 1: In the survey 36% of the men and 50% of the women said that they considered engaging in research an essential goal.
0.36M + 0.50W = # of teachers who consider research essential.
Well, we're already told that 42% of all 1400 teachers consider research essential.
So, 0.36M + 0.50W = (0.42)(1400)

So we have W + M = 1400 and 0.36M + 0.50W = (0.42)(1400)
Since we could solve this system for M and W, we can definitely answer the target question with certainty.
This means that statement 1 is SUFFICIENT

Statement 2: In the survey, 288 men said they considered engaging in research an essential goal.
We don't know the number of men altogether, so we don't know the percentage of men who consider research essential. Plus, we don't know anything about the women.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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Of the 1400 college teachers surveyed, 42% said they considered engagi 17 Aug 2025, 00:23
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