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At a certain company, a test was given to a group of men and women see

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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 26 Nov 2015, 02:10
1
kirtivardhan wrote:
Hi Bunnel,

When you say the average of men is 75 , the average of women is X and the average of the group as 80 can X be less that 85.

Are we trying to combine the averages of the two groups i.e (75+X)/2=80 ?

If so doesn't this take the form of weighted average?


Hi, its indeed a wted average problem. We know how weights affect the wted average. For instance, if avg for men and women were 75 and 85 respectively and if there were more men than women, the weighted avg would be closer to 75 and hence would be less than 80. But since its given that the weighted average is 80, to make 75 relatively closer to 80 we will have to move the avg for women farther away i.e. more than 85. Does that make sense?
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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 31 Oct 2016, 17:18
This answer appears to be long because I have written out my thought pattern and assumptions. The computation can be done in less than a minute. If you also consider that you can spend less than a minute to realize the two statements are not sufficient alone then, this approach can solve the question in less than 2 minutes. While I like the conceptual approaches suggested by others, the skill may not be easily transferable when the structure of the question changes. This is why I prefer the algebraic approach. I missed the question when I took the practice test but after repeated attempts during my review, I came up with the explanation below. I hope someone finds it helpful.
--
Since it is clear that neither statement 1 nor 2 is sufficient alone, I will examine the combined scenario. From what we remember about weighted averages:

Sum of Men's scores + Sum of Women's scores = Sum of scores for the entire group

Since "Sum of Men's scores = Avg for Men * # of men"
and "Sum of Women's scores = Avg for Women * # of women"
we can re-write as:


74(M) + X(W) = 80(M+W)
74(M) + X(W) = 80M + 80W

where X is Women's average and M and W are numbers of men and women respectively.

From what we know about weighted averages if 80M is greater than 74M then X(W) must be greater than 80W and we can move like terms around i.e.:

X(W) - 80W = 80M - 74M
X(W) - 80W = 6M

We can re-write X(W) - 80W as Y(W) where "Y" is the difference between X and 80. Remember we assumed (correctly) that X(W) must be greater than 80(W) i.e.:

Y(W) = 6M

Now, statement 2 says M is greater than W. Therefore, for Y(W) = 6M to be true while M>W, Y has to be significantly greater than 6. Remember Y is the difference between Women's average and the group's. Women's average has to be (>80+6). The least Y can be is 87 and this answers the question satisfactorily i.e. Women's average is greater than 85.

Our answer is therefore "C."
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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 21 Jan 2017, 08:44
My thinking =>

Avg (M+W) = 85.
Is Avg W > 85.
S-1) Avg M < 75. Here we can have 3 cases
M = W - Yes Avg Women Score > 85
M < W - No Avg Women Score < 85
M > W - Yes Avg W Score > 85

Not sufficient as we don’t know Men > Women or vice versa

S-2) Men > Women. No other details. Not sufficient

S-3) Yes since M>W means to make the Avg 80 with Men Score < 75, women score must be > 85

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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 23 Feb 2017, 03:02
Hi, is there a compilation of similar questions that anyone can share?
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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 09 Mar 2017, 01:38
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This question can easily be solved using the alligation diagram.

Before I jump in to solve this question, let me provide you a brief explanation of how to approach weighted average questions on the GMAT. Weighted average questions can be easily solved by making use of the alligation/mixture diagram given below.

Attachment:
Mixtures 1.png
Mixtures 1.png [ 6.07 KiB | Viewed 709 times ]


Putting in values in the alligation/mixture diagram and subtracting along the diagonals gives us a ratio in which two quantities are mixed. This ratio can now be used to find out what specific amounts of two quantities need to be mixed to obtain a particular mixture.

The only thing that you need to keep in mind here is that the values you need to use, that is the higher value, lower value and mean value have to be values which are associated with the word 'per' (percents, average, per km, per kg etc.).

The alligation/mixture diagram proves useful not only when mixing solutions or combining solids but also to explain the weighted average concept (the word average is also associated with the word per i.e. if the average marks of the class is 80, then it can be understood as 80 marks per student). Say if we have a class A where the average marks is 80 and another class B where the average marks is 70 and the combined average of both class A and B is 74, then we can definitely comment upon which class has the greater number of students. If we represent the average values in the mixture diagram, the ratio of students of Class A and Class B will be 2 : 3. This clearly indicates that class B has the greater number of students.

Now the question here tells us that the overall average (mean value) of the group is 80 and we are asked to answer if the average score of the women is greater than 85.

Statement 1 : The average score for the men was less than 75

Attachment:
Mixtures 2.PNG
Mixtures 2.PNG [ 17.56 KiB | Viewed 707 times ]


Here we do not have any information about the ratio of men to women. So we ca consider any value for the average score of women. Insufficient.

Statement 2 : The group consisted of more men than women

Attachment:
Capture 3.PNG
Capture 3.PNG [ 14.98 KiB | Viewed 707 times ]


So if the ration of W : M is 1 : 2, then the average score of the women will be 82 and the average score of the men will be 81 which gives us a NO.

If the ratio of W : M is 1 : 7, then the average score of the women will be 87 and the average score of the men will be 81 which gives us a YES. Insufficient.

Combining 1 and 2 : We know that the average score for the men was less than 75 and the number of men is greater than the number of women.

Attachment:
Combined.PNG
Combined.PNG [ 34.91 KiB | Viewed 707 times ]


So the average score for the women will always be greater than 85. Sufficient.
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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 23 Mar 2017, 13:32
1
I solve this intuitively.
(1) insuff
(2) Insuff

(1)&(2) combined: notice that if you have 50% Men and 50% women then average of women must be 85%
Just because (50%*75 + 50%*W) = 80 leads to W= 85.

Now if you increase the percentage of Men then the average of the Group will decrease.
(Think of the balance) it will balance in favor or the heavier weight.

If you want the balance to remain at 80 while you increase the weight of men then you need to increase average of women above 85.

----Average of Men was less than 75
----There are more Men than Women
----Average of the group is 80

Therefore average of women is greater than 85.

Answer is C.
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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 01 Jul 2017, 23:01
CrackVerbalGMAT wrote:
This question can easily be solved using the alligation diagram.

Before I jump in to solve this question, let me provide you a brief explanation of how to approach weighted average questions on the GMAT. Weighted average questions can be easily solved by making use of the alligation/mixture diagram given below.

Attachment:
Mixtures 1.png


Putting in values in the alligation/mixture diagram and subtracting along the diagonals gives us a ratio in which two quantities are mixed. This ratio can now be used to find out what specific amounts of two quantities need to be mixed to obtain a particular mixture.

The only thing that you need to keep in mind here is that the values you need to use, that is the higher value, lower value and mean value have to be values which are associated with the word 'per' (percents, average, per km, per kg etc.).

The alligation/mixture diagram proves useful not only when mixing solutions or combining solids but also to explain the weighted average concept (the word average is also associated with the word per i.e. if the average marks of the class is 80, then it can be understood as 80 marks per student). Say if we have a class A where the average marks is 80 and another class B where the average marks is 70 and the combined average of both class A and B is 74, then we can definitely comment upon which class has the greater number of students. If we represent the average values in the mixture diagram, the ratio of students of Class A and Class B will be 2 : 3. This clearly indicates that class B has the greater number of students.

Now the question here tells us that the overall average (mean value) of the group is 80 and we are asked to answer if the average score of the women is greater than 85.

Statement 1 : The average score for the men was less than 75

Attachment:
Mixtures 2.PNG


Here we do not have any information about the ratio of men to women. So we ca consider any value for the average score of women. Insufficient.

Statement 2 : The group consisted of more men than women

Attachment:
Capture 3.PNG


So if the ration of W : M is 1 : 2, then the average score of the women will be 82 and the average score of the men will be 81 which gives us a NO.

If the ratio of W : M is 1 : 7, then the average score of the women will be 87 and the average score of the men will be 81 which gives us a YES. Insufficient.

Combining 1 and 2 : We know that the average score for the men was less than 75 and the number of men is greater than the number of women.

Attachment:
Combined.PNG


So the average score for the women will always be greater than 85. Sufficient.

Wow, great explanation! Thanks a lot

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Re: At a certain company, a test was given to a group of men and women see  [#permalink]

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New post 19 Jul 2018, 08:50
for statement 1&2: I tried using weighted average

Let x be the average score of women
M/W = (X - 80)/ (80 -75) = a/5
because the number of men is gretear than women hence, a must be greater than 5. So X must be gretear than 85.

Hence Sufficient. C is the ans

Please correct me if my method is wrong.
Re: At a certain company, a test was given to a group of men and women see &nbs [#permalink] 19 Jul 2018, 08:50

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