GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jul 2018, 14:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 Aug 2010
Posts: 234
The average weight of the women in a room is 120 lbs, and [#permalink]

### Show Tags

10 Jan 2011, 18:55
9
00:00

Difficulty:

15% (low)

Question Stats:

71% (00:30) correct 29% (00:37) wrong based on 295 sessions

### HideShow timer Statistics

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.

_________________

Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Math Expert
Joined: 02 Sep 2009
Posts: 46991
Re: The average weight of the women in a room [#permalink]

### Show Tags

11 Jan 2011, 01:19
3
2
ajit257 wrote:
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.

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.

_________________
##### General Discussion
Manager
Joined: 28 Aug 2010
Posts: 234
Re: The average weight of the women in a room [#permalink]

### Show Tags

12 Jan 2011, 18:49
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
_________________

Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Math Expert
Joined: 02 Sep 2009
Posts: 46991
Re: The average weight of the women in a room [#permalink]

### Show Tags

13 Jan 2011, 01:37
ajit257 wrote:
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

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).
_________________
VP
Joined: 24 Jul 2011
Posts: 1439
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: The average weight of the women in a room is 120 lbs, [#permalink]

### Show Tags

26 Nov 2011, 02:26
1
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.
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Intern
Joined: 11 Nov 2011
Posts: 14
Re: The average weight of the women in a room is 120 lbs, [#permalink]

### Show Tags

26 Nov 2011, 04:56
1
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

Intern
Joined: 22 Jul 2014
Posts: 10
The average weight of the women in a room is 120 lbs, and [#permalink]

### Show Tags

22 Aug 2015, 13:13
[quote="Bunuel"][quote="ajit257"]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
_________________

- The race is on .. ..

Consider to give a kudo if the post helped !

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11957
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: The average weight of the women in a room is 120 lbs, and [#permalink]

### Show Tags

22 Aug 2015, 15:27
2
1
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...

2 men and 1 woman
the average would be [2(150)+1(120)]/3 = 420/3 = 140 pounds

4 men and 2 women
the average would be [4(150)+2(120)]/3 = 840/6 = 140 pounds

6 men and 3 women
the average would be [6(150)+3(120)]/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...

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

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 18 May 2015
Posts: 12
Re: The average weight of the women in a room is 120 lbs, and [#permalink]

### Show Tags

14 May 2016, 09:19
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.
Math Expert
Joined: 02 Aug 2009
Posts: 6196
Re: The average weight of the women in a room is 120 lbs, and [#permalink]

### Show Tags

14 May 2016, 09:36
oa7 wrote:
Where I get confused is with Fact 1 (There are twice as many men as women in the room.)
Edit:

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.

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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Non-Human User
Joined: 09 Sep 2013
Posts: 7241
Re: The average weight of the women in a room is 120 lbs, and [#permalink]

### Show Tags

05 Oct 2017, 10:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The average weight of the women in a room is 120 lbs, and   [#permalink] 05 Oct 2017, 10:34
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.