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The average weight of the men in a meeting room is 170 pounds and the

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Bunuel
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The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   08 Jul 2019, 02:46
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The average weight of the men in a meeting room is 170 pounds and the average weight of the women is 130 pounds. If more than 60% of the people in the room are men, which of the following could be the average weight of all people in the room?

I. 156
II. 158
III. 168

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
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E
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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   08 Jul 2019, 03:00
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Bunuel wrote:
The average weight of the men in a meeting room is 170 pounds and the average weight of the women is 130 pounds. If more than 60% of the people in the room are men, which of the following could be the average weight of all people in the room?

I. 156
II. 158
III. 168

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


Average when men = 60%
= 170*0.6 + 130*0.4 = 102 + 52 = 154
So, average will be >154

Average when men = 100%
= 170

So, all values of average are possible

IMO Option E

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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   08 Jul 2019, 03:04
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Lets find out the minimum possible overall average, which when men are 60%

Ratio of men to women is 60/40=3/2

Set up the weighted average equation where x is considered the required overall weighted average

3/2 = (x-130)/(170-x)

Solving the above, we get x=154

Thus the weighted average when men are at minimum constraint is 154.

Since the men weigh more than 154, as the number of men increses, the average weight is pulled closer to the average weight of men (170 pounds)

Thus any value above 154 is possible to be the overall average

Answer is (E)

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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   08 Jul 2019, 10:08
Bunuel wrote:
The average weight of the men in a meeting room is 170 pounds and the average weight of the women is 130 pounds. If more than 60% of the people in the room are men, which of the following could be the average weight of all people in the room?

I. 156
II. 158
III. 168

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


total 10 people
so supposedly so if .6*170+130*.4 ; 102+52;154
so avg has to be >154 for >60% men ; IMO E
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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   11 Jul 2019, 20:07
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Bunuel wrote:
The average weight of the men in a meeting room is 170 pounds and the average weight of the women is 130 pounds. If more than 60% of the people in the room are men, which of the following could be the average weight of all people in the room?

I. 156
II. 158
III. 168

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


Let’s first calculate the minimum possible weighted average and then the maximum possible weighted average.

If exactly 60% are men and 40% are women, then the average weight of all people in the room is:

0.6 x 170 + 0.4 x 130 = 102 + 52 = 154

However, if 100% of the people in the room are men, then the average is 170.

Thus, the weighted average can be anything greater than 154 and up to 170.

Thus, 156, 158, and 168 are all possible weighted averages.

Answer: E
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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   11 Jul 2019, 22:20
Bunuel wrote:
The average weight of the men in a meeting room is 170 pounds and the average weight of the women is 130 pounds. If more than 60% of the people in the room are men, which of the following could be the average weight of all people in the room?

I. 156
II. 158
III. 168

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


When 60% are men and 40% are women
Average weight = 60%*170+40%*130 = 154 pounds

When 100% are men
Average weight = 170 pounds

All values of average between 154 and 170 pounds are possible.

IMO E
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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   16 Sep 2021, 19:40
is there anyother way to solve this with out using weighted average ?
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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink] New post   16 Sep 2021, 21:27
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saad166 wrote:
is there anyother way to solve this with out using weighted average ?


The question is looking for the weighted average of the room. No matter what you do and what you call it, you would be using the weighted average concept.

The average will lie between 130 and 170 depending on how many men and women there are.

If 60% were men,
Avg = (170*60% of Total + 130 * 40% of Total)/Total = (510 + 260)/5 = 770/5 = 154

Since men are more than 60%, avg will be more than 154 but less than 170 (if there is at least 1 woman).
Hence all three options are possible.

Answer (E)
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Re: The average weight of the men in a meeting room is 170 pounds and the [#permalink]
16 Sep 2021, 21:27
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