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Re: At a certain company, a test was given to a group of men and women see
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26 Nov 2015, 01:10
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
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16 Aug 2016, 05:27
Here is how I solved it in under 1 minute:
Provided from prompt: 80 = Scores of M+W / # M + W (W/# M + W * Women Average) + (M/# M + W * Men Average) = 80 Is Women Average > 85?
Statement 1) The average score for the men was less than 75
Men Average < 75 Let's assume 74 . . . 74 is 6 away from 80. Therefore, we need women's average to compensate for that. If we have 1 women and 1 men in the group, Men = 74, Women = 86. Average = 80.
Is W > 85  Yes
Now what would happen if there are 2 women and 1 man? Men = 74, then both women have to compensate for a total of 6, or 3 each. Thus, each women will have a score of 83. Men = 74, Women = 83 + 83/2 = 83
Is W>85  No
Insufficient.
Statement 2) The group consisted of more men than women.
We know nothing about their individual averages. Insufficient.
S 1&2) As you could see from our counter examples in statement 1, if we have more women than men, average of women will be <85, however; if we have more men than women, average of women has to be >85. See below.
2 Men = 74, 74 Each man contributes to 6 units away from 80. Therefore, 12 units in total. Since, M > W, we can have a maximum of 1 W in this example. That 1 woman has to make up 12 units for the average of the entire group to be 80. Thus,
Women = 80+12 = 92
Is W > 85  Yes, absolutely, always.
You can take a number of examples. The pattern to recognize here is; the less the average in Men, the higher average in Women is expected to make up for the loss in men for the average to be 80. If we have less men, we need women to make up for the difference between the groups average and the mens average.
Hope this helps!



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Re: At a certain company, a test was given to a group of men and women see
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31 Oct 2016, 16:18
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 rewrite 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 rewrite 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
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21 Jan 2017, 07:44
My thinking => Avg (M+W) = 85. Is Avg W > 85. S1) 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 S2) Men > Women. No other details. Not sufficient S3) Yes since M>W means to make the Avg 80 with Men Score < 75, women score must be > 85 Thanks, Coolkl
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Re: At a certain company, a test was given to a group of men and women see
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23 Feb 2017, 02:02
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
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09 Mar 2017, 00:38
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 [ 6.07 KiB  Viewed 810 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 75Attachment:
Mixtures 2.PNG [ 17.56 KiB  Viewed 808 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 womenAttachment:
Capture 3.PNG [ 14.98 KiB  Viewed 808 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 [ 34.91 KiB  Viewed 808 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
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23 Mar 2017, 12:32
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
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01 Jul 2017, 22:01
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 75Attachment: 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 womenAttachment: 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 Sent from my SMG900F using GMAT Club Forum mobile app



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Re: At a certain company, a test was given to a group of men and women see
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19 Jul 2018, 07:50
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
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