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

It is currently 18 Nov 2019, 14:52

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A total of 22 men and 26 women were at a party, and the average

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59125
A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 20 Oct 2015, 03:06
5
38
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

71% (02:36) correct 29% (02:44) wrong based on 993 sessions

HideShow timer Statistics

A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.

_________________
Most Helpful Community Reply
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 818
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 20 Oct 2015, 06:18
8
9
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


One can use the weighted average method:

\(\frac{Weight 1}{Weight 2} = \frac{Average2-Average}{Average-Average1}\)

For or example:

\(\frac{26}{22} = \frac{38-35}{35-Average1}\)

Solving for Average1 you will get exactly 32.46154. Answer D.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
General Discussion
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2431
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 20 Oct 2015, 03:43
4
9
Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people

35 * 48 = 22 * 38 + 26 * Aw
=>1680 = 836 + 26 Aw
=> 26 Aw = 844
=>Aw = 32.5

Answer D


Scale method -
If number of men and women were equal , the average would have been at the center of the average age of the individual groups
Average age of women = 32 as 35 will be equidistant from 32 and 38 (average age of men)
At this point we can eliminate A , B and C

But since , number of women are more , average age will be more than 32
Ratio of women to men = 26:22 = 13:11
If Aw= 32.5
Distance from the average
35- 32.5 :38-35
2.5 :3
5:6
which is rougly equal to inverse of 13:11

Answer D
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 818
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 20 Oct 2015, 07:09
4
2
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


You can also think of it like this on a scale method base:

x(Average female)..........(35-x)............Average(35)..........(3)............(38)Average male
#26 (No. of females)..........................................................................#22 (No. of males)

So again this shows that we have to groups which mixed together have an a weighted average of 35. The "weighs" in this example are the number of people. For men 22 and for woman 26. You can now equate the known weighs with the differences to average:

\(\frac{26}{22}=\frac{3}{(35-x)}\)

Then solve for x to get x= 32.4615

Answer D.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 20 Oct 2015, 07:40
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.




38*22 + W*26 = 35*(22+26)
i.e. W = 844/26 = 32.46 = 32.5

Answer: option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4065
Location: Canada
A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post Updated on: 06 Mar 2018, 10:49
2
2
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

There are 48 people in total.
So, 22/48 = the proportion of women
And 26/48 = the proportion of men

Let x = average age of the women

So, plugging the information into the formula, we get: (22/48)(38) + (26/48)(x) = 35
Simplify: (11/24)(38) + (13/24)(x) = 35
Multiply both sides by 24 to get: (11)(38) + 13x = (35)(24)
Simplify: 418 + 13x = 840
Rearrange: 13x = 422
Solve: x = 422/13 ≈ 32.5

Answer: D

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image

Originally posted by GMATPrepNow on 20 Oct 2015, 08:03.
Last edited by GMATPrepNow on 06 Mar 2018, 10:49, edited 1 time in total.
Manager
Manager
avatar
P
Joined: 01 Mar 2015
Posts: 68
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 21 Oct 2015, 04:54
1
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


let average age of women be x

then, we have

\(22 * 38 + 26 * x = 48 * 35\)

=> \(x = 32.46\)

Answer choice D
Intern
Intern
avatar
Joined: 09 Nov 2015
Posts: 1
GPA: 3.56
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 19 Mar 2016, 11:41
1
I followed a similar approach to the scale. Given that m:w is 11:13 and we know that the AVG(m) = 38 and AVG(m+w)=35. We already know the AVG(w) has to be less than 35 given the higher weighting to w. I ended up multiplying the (11/13) * 38. To simplify, I rounded to redo the formula as (11/13)*39 = 33. Therefore, the answer must be just under 33 or 32.5. Also, keep in mind the key word of "closest", which implies that you do not need an EXACT answer (no crazy math).
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8411
Location: United States (CA)
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 04 May 2016, 09:55
1
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


1) Since there are 48 people (22 men and 26 women) and the average age of all of them is 35, the total ages of all the people at the party is 48(35).

2) Since there are 22 men and their average age is 38, the sum of all the men's ages is 22(38).

3) There are 26 women; letting their average age be x, the sum of all the women's ages is 26x.

Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have

48(35) = 22(38) + 26x

1680 = 836 + 26x

26x = 844

x = 844/26

x = 32 12/26 ≈ 32.5

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4831
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 04 May 2016, 10:23
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


Total age of men and women = 48*35 => 1,680

Total age of men is = 22*38 => 836

So, total age of women in = 1680 - 836 => 844

Average age of women is 844/26 => 32.46

Hence answer will be (D) 32.5 :P
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Manager
avatar
B
Joined: 18 Aug 2013
Posts: 121
Location: India
Concentration: Operations, Entrepreneurship
GMAT 1: 640 Q48 V28
GPA: 3.92
WE: Operations (Transportation)
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 16 May 2016, 20:05
7
Here is the MGMAT Solution to it.

Avg. age of men is +3 than the avg. age of the group.

Now,

3(22)+w(26)=0....(Make this differential cancel out,hence equal to 0)

22=no. of men
26=no. of women
3=differential from mean.

Hence w=-2.5

Thus group mean (35)+Differential (-2.5)=32.5

Hope its simple than all the long calculations.
Retired Moderator
avatar
P
Joined: 17 Jun 2016
Posts: 499
Location: India
GMAT 1: 720 Q49 V39
GMAT 2: 710 Q50 V37
GPA: 3.65
WE: Engineering (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 11 Aug 2016, 06:42
1
3
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


I uesd the Std Deviation method :
Ave of Man = 38 (which is 38-35 = 3 more than the ave of Man & Women together)
and No of man = 22
Therefore Deviation More than the Mean = 3 * 22 = 66

Also, we know that No of women = 26
Now, For any given set of numbers, Deviation More than the Mean is ALWAYS = Deviation Less than the Mean
Therefore, each women can have a deviation of = 66/26 ~= 2.5 from the Average Value
Therefore, Ave age of Women = 35-2.5 = 32.5

Kudos if u like the method....
Manager
Manager
User avatar
G
Joined: 30 Dec 2015
Posts: 81
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Premium Member
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 09 Oct 2016, 16:02
1
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


It initially took mme ~2mins to solve this, but tried a couple of ways and think weighted avg would be fastest as lesser big numbers to deal with:

[Women-avg: (w)]----------------35--------------------38

\(\frac{26}{22} = \frac{3}{(35-w)}\)
\(w = 35 - \frac{33}{13}\)
13 * 2 = 26; hence \(\frac{33}{13} = 2.x\) (I wont even bother getting the decimal)
w = 35 - 2.x = 32.x (~32.5)
_________________
If you analyze enough data, you can predict the future.....its calculating probability, nothing more!
Intern
Intern
avatar
B
Joined: 25 Jan 2018
Posts: 8
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 17 May 2019, 19:18
Hi there :)

Could you explain the logic behind this ratio formula please? Thanks so much!!
reto wrote:
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


One can use the weighted average method:

\(\frac{Weight 1}{Weight 2} = \frac{Average2-Average}{Average-Average1}\)

For or example:

\(\frac{26}{22} = \frac{38-35}{35-Average1}\)

Solving for Average1 you will get exactly 32.46154. Answer D.


Posted from my mobile device
Read Only User
Read Only User
avatar
S
Status: booyeh!
Joined: 26 May 2017
Posts: 16
Location: India
Concentration: Strategy, Marketing
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 17 May 2019, 20:50
2
average age of man * number of men = summation of ages of men
average age of woman * number of women = summation of ages of women

summation of ages of men + summation of ages of women = summation of ages of men and women

Thus, (38*22) + (average age of woman*26) = 35*(22+26)

simplifying,
average age of woman = {[35*(22+26)]-(38*22)}/26 = a little greater than 32 => 32.5


Answer: D
Manager
Manager
avatar
B
Joined: 03 Aug 2017
Posts: 79
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 11 Oct 2019, 03:46
GMATPrepNow wrote:
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

There are 48 people in total.
So, 22/48 = the proportion of women
And 26/48 = the proportion of men

Let x = average age of the women

So, plugging the information into the formula, we get: (22/48)(38) + (26/48)(x) = 35
Simplify: (11/24)(38) + (13/24)(x) = 35
Multiply both sides by 24 to get: (11)(38) + 13x = (35)(24)
Simplify: 418 + 13x = 840
Rearrange: 13x = 422
Solve: x = 422/13 ≈ 32.5

Answer: D

Cheers,
Brent


How can we assume that 35 is the weighted average and not a simple avg of 48 people in total ?
Intern
Intern
avatar
B
Joined: 10 Jul 2018
Posts: 5
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 19 Oct 2019, 08:21
It is given that the exact age of men is 38, whereas the average age of man and women is 35. That means, every man sacrifice 3 years to set the given average i.e 35. Mathematically, from the age of 22 men, we get 66 years to be added up to the age of woman. As there are 26 woman, each one gets 2.7/13 years. Thus the age of a woman is 35- 2.7/13 = 32.50 years.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4065
Location: Canada
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 21 Oct 2019, 15:28
Top Contributor
mimajit wrote:
How can we assume that 35 is the weighted average and not a simple avg of 48 people in total ?


The average = 35 = weighted average
They are the same thing.
The "weight" here is dictated by the number of women compared to the number of men.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
B
Joined: 05 Apr 2019
Posts: 1
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 21 Oct 2019, 18:13
average age- 35
22 man adds extra 22*3=66 yrs.
26 women must neutralize 66 years. so (35-32.5=2.5)
2.5*26=65 (closest to 66)
so 32.5 is the answer
Director
Director
User avatar
P
Joined: 18 Dec 2017
Posts: 700
Location: United States (KS)
Premium Member
Re: A total of 22 men and 26 women were at a party, and the average  [#permalink]

Show Tags

New post 29 Oct 2019, 12:26
Bunuel wrote:
A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?

(A) 31
(B) 31.5
(C) 32
(D) 32.5
(E) 33

Kudos for a correct solution.


I solved it in 49 seconds and here is the approach.

Average Age = 35.

22 people have contributed = +3 each. Which means we are 66 above the average.

26 people have to reduce the total of their age by 66 to keep the average intact at 35.

66/26=33/13=2.53=2.5

So each goes 2.5 below the average which is 35.

Hence 32.5

Answer D
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Software Tester currently in USA ( ;-) )

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
GMAT Club Bot
Re: A total of 22 men and 26 women were at a party, and the average   [#permalink] 29 Oct 2019, 12:26
Display posts from previous: Sort by

A total of 22 men and 26 women were at a party, and the average

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne