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

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.

How many of the college teacher surveyed were women? The question does not mention research. The answer should be E.

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

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.

Posted from my mobile device

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?

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.

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.

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.

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 !

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 \(1400*0.42=0.36*m+0.5*w\).

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.

Answer: Option A

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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

Cheers,
Brent

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