The average weight of the women in a room is 120 lbs, and

Question

The average weight of the women in a room is 120 lbs, and the average weight of the men in the room is 150 lbs. What is the average weight of the people in the room?

(1) There are twice as many men as women in the room.

(2) There are a total of 120 people in the room.

Bunuel, please can you clarify when to take a problem as average weight and when to take it as a normal average problem. I have to divulge details so i apologize as I just wanted to clarify a concept. So i understand that if you have to average the total of 2 quantities you need the total of A and total of B. Hence i am confused here. so here would you not need the total women and total men then get the respective weights and then average. Would appreciate your help.

Bunuel · Accepted Answer

Any average equals to  average=\frac{total \ weight}{sum \ of \ values}  (I think this is what you call "normal average"). When you have two values (boys and girls for example) then the formula can be written as  weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}  note that it's the same  \frac{total \ weight}{# \ of \ values} .

Back to the question:

The average weight of the women in a room is 120 lbs, and the average weight of the men in the room is 150 lbs. What is the average weight of the people in the room?

The average weight of the women in the room is 120 lbs -->  average_{women}=120=\frac{total \ weight}{# \ of \ women} , let # of women be  w  -->  total \ weight=120w ;
The average weight of the men in the room is 1500 lbs -->  average_{women}=150=\frac{total \ weight}{# \ of \ women} , let # of men be  m  -->  total \ weight=150m ;

Question:  average_{all}=\frac{total \ weight}{# \ of \ values}=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}=\frac{120w+150m}{w+m} ?

(1) There are twice as many men as women in the room --> knowing individual averages (120 and 150) and the ratio of the values (w/m=1/2) is always sufficient to get the weighted average:  m=2w  -->  average_{all}=\frac{120w+150*2w}{w+2w}=\frac{120+150*2}{3}=140 . Sufficient.
 
(2) There are a total of 120 people in the room -->  w+m=120 , not sufficient.

Answer: A.

ajit257 · Answer

thanks! Bunuel. So here i have a doubt. If we have to calculate the total average value of 2 quantities and we are given the average of both the quantities then don't we find the the total of first quant and the total of second quant and then the grand sum total/ total(a) + total(b). This is where my confusion is (ie one cannot take the average of both quantities and then average them out). Please advise

Bunuel · Answer

Not sure understood your question.

Please read this again:  any average  equals to  average=\frac{total \ weight}{# \ of \ values}  (for example: average speed in mile/hour=total distance covered in miles/# of hours spent or average salary=total salary/# of employees ... I think this is what you call "normal average"). When you have two values (boys and girls for example) then the formula can be written as  weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2}  note that it's the same  \frac{total \ weight}{# \ of \ values}  (nominator gives total weight and denominator gives total # values).

GyanOne · Answer

Clearly (A).

Using statement (1), we can easily calculate the weighted average of the people in the room. Sufficient. 
Using statement (2), we don't know the split between the number of men/women so we cannot calculate the overall average. Insufficient.

bobfirth · Answer

Average of the Group = (weight of all women + weight of all men)/size of group

From 1. we can get:
weight of all women = 120 x (size of group x 1/3) = 40 x size of group
weight of all women = 150 x (size of group x 2/3) = 100 x size of group

therefore
Average of the Group = (40 x size of group + 100 x size of group)/size of group = 140

SUFFICIENT

2. the total number of people in the group does not give us enough information to figure out the average weight of the group. For example:
If 1 woman and 119 men average will be very close to 150.
If 119 women and 1 man, average will be very close to 120.
INSUFFICIENT

So the answer is A.

PratikHP · Answer

The average weight of the women in a room is 120 lbs, and the average weight of the men in the room is 150 lbs. What is the average weight of the people in the room?
 
(1) There are twice as many men as women in the room.
 
(2) There are a total of 120 people in the room.

Weighted average:  \frac{120W+150M}{W+M}

A)  Sufficient: 
It is subtle but a good point to note here is that the comparison of women to men is in absolute value "twice". Had the statement mentioned that the ratio of women to men then it would've been insufficient.

Now given:
=>  2W=M 
=>  Avg. =   \frac{120W+150*2W}{W+2W} 
=>  Avg. =  140

B)  Insufficient

W + M=120  ( No absolute value for M or W) 
One equation two variable. Hence insufficient.

Ans: A

Regards,
Pratik

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing VALUES.

We're given two pieces of information to work with:
1) The average weight of the women in a room is 120 pounds
2) The average weight of the men that same room is 150 pounds

We're asked for the average weight of ALL the people in that room.

Fact 1: There are twice as many men as women in the room.

With this ratio, we can prove that the average weight is always the same. Here's how...

IF we had....
2 men and 1 woman
the average would be  /3 = 420/3 = 140 pounds

4 men and 2 women
the average would be  /3 = 840/6 = 140 pounds

6 men and 3 women
the average would be  /9 = 1260/9 = 140 pounds

The average is ALWAYS 140 pounds.
Fact 1 is SUFFICIENT

Fact 2: There are a total of 120 people in the room.

The average will vary depending on how many men and women are in the room...

IF we had....
60 men and 60 women
the average would be exactly 'in the middle' = 135 pounds

61 men and 59 women
the average would be something other than 135 pounds
Fact 2 is INSUFFICIENT

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

oa7 · Answer

Where I get confused is with Fact 1 (There are twice as many men as women in the room.)

To me that translates to a ratio of W:2M. However, as posted with answers to this question, the ratio is supposed to be 2W:M. I don't understand how.

chetan2u · Answer

Hi,

There are twice as many men as women in the room...
this means there are twice men, that is the number of men is MORE..
How much twice
so M = 2W

CEdward · Answer

Weighted averages.

The average weight of the women in a room is 120 lbs, and the average weight of the men in the room is 150 lbs. What is the average weight of the people in the room?

(1) There are twice as many men as women in the room.
120F + 150(2F) / 3F ...
Sufficient

(2) There are a total of 120 people in the room.
M + F = 120 ---> F = 120 - M
120 (120 - M) + 150M / 120
One variable left over that we don't know (M)

Insufficient.

A.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The average weight of the women in a room is 120 lbs, and

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

The average weight of the women in a room is 120 lbs, and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards