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## og13 men and women seeking promotions

This topic has 2 expert replies and 6 member replies
gtr02 Senior | Next Rank: 100 Posts
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Posted:
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#### og13 men and women seeking promotions

Sat May 05, 2012 1:13 pm
ds70

at a certain company, a test was given to a group of men and women seeking promotions. if the avg score for the group was 80, was the avg score for the women greater than 85?

1) the avg score for the men was less than 75
2) the group consisted of more men than women

OA after a few posts, had a tough time with this one

OA: c

Last edited by gtr02 on Sun May 06, 2012 12:11 pm; edited 1 time in total

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Liarish Newbie | Next Rank: 10 Posts
Joined
17 May 2012
Posted:
6 messages
Tue Nov 06, 2012 9:19 am
Hi Mitch,

Great explanation. I have a question though.

I understand why statement 1 is Not Sufficient.
But Does Statement 1 mean that : because the average score for the entire group=80, and average score (men)< 75, should the average score(women) MUST be more than 80?
(although this does not give us enough information to prove that average score(women)> 85). Hope I haven't confused you!

FLUID Senior | Next Rank: 100 Posts
Joined
01 Nov 2012
Posted:
39 messages
7
Tue Nov 06, 2012 8:33 pm
ds70

at a certain company, a test was given to a group of men and women seeking promotions. if the avg score for the group was 80, was the avg score for the women greater than 85?

1) the avg score for the men was less than 75
2) the group consisted of more men than women

average score of group = 80
Avg. women score > 85?

From statement 1, we know that avg score for men is < 75

Since we don't know the count of women and men , it is not SUFFICIENT.

From statement 2, the group consisted of more men than women

Suppose, There are 2 Men (M1 and M2) and 1 Women ( W1).

(M1+ M2 + W1) /3 = 80 ( As per the question)

From statemen1, (M1 + M2)/2 < 75.
=> M1+M2 < 75 * 2 => M1+M2 < 150

Suppose, M1+ M2 scored 149 since average of group is 80

149+ W1/3 = 80 => W1 = 91
This means that if men scored 149 women scored 91. So, minimum score of the women is 91
=> Womens Averge score is > 85

Answer is (c) since we have used statement1 and statement 2.

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Liarish Newbie | Next Rank: 10 Posts
Joined
17 May 2012
Posted:
6 messages
Tue Nov 06, 2012 9:19 am
Hi Mitch,

Great explanation. I have a question though.

I understand why statement 1 is Not Sufficient.
But Does Statement 1 mean that : because the average score for the entire group=80, and average score (men)< 75, should the average score(women) MUST be more than 80?
(although this does not give us enough information to prove that average score(women)> 85). Hope I haven't confused you!

FLUID Senior | Next Rank: 100 Posts
Joined
01 Nov 2012
Posted:
39 messages
7
Tue Nov 06, 2012 8:33 pm
ds70

at a certain company, a test was given to a group of men and women seeking promotions. if the avg score for the group was 80, was the avg score for the women greater than 85?

1) the avg score for the men was less than 75
2) the group consisted of more men than women

average score of group = 80
Avg. women score > 85?

From statement 1, we know that avg score for men is < 75

Since we don't know the count of women and men , it is not SUFFICIENT.

From statement 2, the group consisted of more men than women

Suppose, There are 2 Men (M1 and M2) and 1 Women ( W1).

(M1+ M2 + W1) /3 = 80 ( As per the question)

From statemen1, (M1 + M2)/2 < 75.
=> M1+M2 < 75 * 2 => M1+M2 < 150

Suppose, M1+ M2 scored 149 since average of group is 80

149+ W1/3 = 80 => W1 = 91
This means that if men scored 149 women scored 91. So, minimum score of the women is 91
=> Womens Averge score is > 85

Answer is (c) since we have used statement1 and statement 2.

_________________
Thanks,

If you Win, you can Lead!
If you Loose, you can Guide!".

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Wed Nov 07, 2012 7:47 am
If anyone is interested, we have a free and comprehensive video on the topic of weighted averages: http://www.gmatprepnow.com/module/gmat-statistics?id=805

Cheers,
Brent

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GMATGuruNY GMAT Instructor
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Sat May 12, 2012 3:12 am
gtr02 wrote:
ds70

at a certain company, a test was given to a group of men and women seeking promotions. if the avg score for the group was 80, was the avg score for the women greater than 85?

1) the avg score for the men was less than 75
2) the group consisted of more men than women

OA after a few posts, had a tough time with this one

OA: c

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

Tells us only that the average score for the women was greater than 80.

Case 1: 1 man + 1 woman, sum = 2*80 = 160.
Let the man's score = 10.
Then the woman's score = 150.

Case 2: 10 men + 100 women, sum = 110*80 = 8800.
Let the men's average = 70, for a sum of 10*70 = 700.
Sum of the women's scores = 8100.
Women's average = 8100/100 = 81.

Since in the first case the average for the women is greater than 85, and in the second case the average for the women is less than 85, INSUFFICIENT.

The cases above illustrate that the average for the women depends on TWO variables:
1. The DISTANCE between the average for the men and the average for the whole group.
2. The RATIO of men to women -- in other words, how much WEIGHT is given to the men's average.

Statement 2: The group consisted of more men than women.
No way to determine the average for the women.

Statements 1 and 2 combined:
Here we have information about the two variables discussed above.
The DISTANCE between the average for the men and the average for the whole group is greater than 5.
Since there are more men than women, more WEIGHT is being given to the average for the men.
Thus, to compensate, the distance between the average for the women and the average for the whole group must also be greater than 5 -- in fact, it must be greater than the distance between the average for the men and the average for the whole group.
Thus, the average for the women must be greater than 85.
SUFFICIENT.

To illustrate why the two statements combined are sufficient, let's examine two more cases.

If there were an equal number of men and women, and the men's average were exactly 75, then the women's average would be exactly 85.

Case 3: 1 man + 1 woman, sum = 2*80 = 160.
Let the man's score = 75.
Then the woman's score = 85.

But when the statements are combined, the relative number of men INCREASES, and their average score is LESS than 75.
Because MORE WEIGHT is being given to the men's lower scores, the average for the women must compensate by being GREATER than 85.

Case 4: 2 men + 1 woman, sum = 3*80 = 240.
Let's the men's average score = 70, for a sum of 2*70 = 140.
Then the woman's score = 100.

Case 4 illustrates that the average for the women must be GREATER than 85.

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hey_thr67 Master | Next Rank: 500 Posts
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Sun May 06, 2012 8:12 pm
@gtr02:
There are typo errors in my explanation. Sorry, I am re-writing again,

1+2 :
Let us take the best average for men which is 75.

75(m)+AV(w)= 80 (w+m). If m=w then AV(w) = 80x2 - 75 (take the best average for men)
AV(w) = 85
Since AV(m) will always be <75, Av(w) will always be greater than 85. As m increases,we need higher average at women's side to keep the cumulative average as 80.

Thanked by: gtr02
aneesh.kg Master | Next Rank: 500 Posts
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Sat May 05, 2012 3:30 pm
This a classic weighted mean problem.
If we have two categories - in this case Men and Women - the larger weight or the larger fraction will tilt the overall average towards it (just like Scales). More the weight, more is the tilt.

Given:
Average Score of Men and Women = 80
Is the average score of women > 85 ?

Statement(1):
The average score of men is 75.
If Number of Men = Number of Women, average score of women = 85
If Number of Men > Number of Women, average score of women > 85 (because the weightage of men is greater and the overall average (80) should be closer to that of Men(75) than Women(say 88))
If Number of Men < Number of Women, average score of women < 85 (because the weightage of women is greater, the overall average(80) should be further from Men(75) and closer to Women(say 82))
INSUFFICIENT, because we do not know the relation between number of Men and Women.

Statement (2), which in itself is INSUFFICIENT, provides exactly that.

So, Statement(1) upon combining with Statement (2) will answer the question.
The question can now be answered with a YES.

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Aneesh Bangia
GMAT Math Coach
aneesh.bangia@gmail.com

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