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

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Veritas Prep GMAT Instructor
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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28 Apr 2017, 06:08
1
vijaisingh2001 wrote:
(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?

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

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06 Jun 2017, 18:48
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:

$$m+w=1400$$ 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.

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

Thank you Bunuel sir,
Jat
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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23 Jan 2018, 19:57
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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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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23 Jan 2018, 21:42
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sdlife wrote:
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.

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

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15 Aug 2018, 21:24
How many of the college teacher surveyed were women? The question does not mention research. The answer should be E.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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16 Aug 2018, 21:15
s55day wrote:
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
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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13 Oct 2018, 22:47
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
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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08 May 2019, 12:04

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

Can you help me identify my gaps?
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi  [#permalink]

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14 May 2019, 06:44
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Probus wrote:

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

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.
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Re: Of the 1400 college teachers surveyed, 42% said they considered engagi   [#permalink] 14 May 2019, 06:44

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