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

It is currently 20 Apr 2019, 11:46

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. The average (arithmeti

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54376
A total of 22 men and 26 women were at a party. The average (arithmeti  [#permalink]

Show Tags

New post 30 Jun 2017, 02:44
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:44) correct 44% (02:34) wrong based on 57 sessions

HideShow timer Statistics

A total of 22 men and 26 women were at a party. The average (arithmetic mean) age of all of the people at the party was exactly 66.74 years. If the average age of the men was exactly 69.74 years, which of the following was closest to the average age, in years, of the women?

(A) 61.24
(B) 63.74
(C) 64.24
(D) 64.74
(E) 69.24

_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54376
Re: A total of 22 men and 26 women were at a party. The average (arithmeti  [#permalink]

Show Tags

New post 30 Jun 2017, 02:46
Bunuel wrote:
A total of 22 men and 26 women were at a party. The average (arithmetic mean) age of all of the people at the party was exactly 66.74 years. If the average age of the men was exactly 69.74 years, which of the following was closest to the average age, in years, of the women?

(A) 61.24
(B) 63.74
(C) 64.24
(D) 64.74
(E) 69.24


This is a modified question of the the following OG question: https://gmatclub.com/forum/a-total-of-2 ... 07390.html
_________________
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
A total of 22 men and 26 women were at a party. The average (arithmeti  [#permalink]

Show Tags

New post 30 Jun 2017, 03:03
Bunuel wrote:
A total of 22 men and 26 women were at a party. The average (arithmetic mean) age of all of the people at the party was exactly 66.74 years. If the average age of the men was exactly 69.74 years, which of the following was closest to the average age, in years, of the women?

(A) 61.24
(B) 63.74
(C) 64.24
(D) 64.74
(E) 69.24


Total number of people \(= 22 + 26 = 48\)

Average age of all the people \(= 66.74\)

Total sum of ages \(= 66.74 * 48 = 3203.52\)

Average age of the men \(= 69.74\)

Total number of men \(= 22\)

Sum of ages of men \(= 1534.28\)

Sum of ages of women \(= 3203.52 - 1534.28 = 1669.24\)

Total number of women \(= 26\)

Average age of women \(= \frac{1669.24}{26} = 64.20\)

Closest value \(= 64.24\)

Answer (C)...
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4419
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User CAT Tests
Re: A total of 22 men and 26 women were at a party. The average (arithmeti  [#permalink]

Show Tags

New post 30 Jun 2017, 11:11
Bunuel wrote:
A total of 22 men and 26 women were at a party. The average (arithmetic mean) age of all of the people at the party was exactly 66.74 years. If the average age of the men was exactly 69.74 years, which of the following was closest to the average age, in years, of the women?

(A) 61.24
(B) 63.74
(C) 64.24
(D) 64.74
(E) 69.24

\((22+26)*66.74 = 22*69.74 + 26*w\)

Or, \(3203.52 = 1534.28 + 26w\)

Or, \(w = \frac{3203.52 - 1534.28}{26}\)

Or, \(w = 64.20\)

Thus, the correct answer will be (C)

_________________
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 )
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2642
A total of 22 men and 26 women were at a party. The average (arithmeti  [#permalink]

Show Tags

New post 30 Jun 2017, 11:45
1
Bunuel wrote:
A total of 22 men and 26 women were at a party. The average (arithmetic mean) age of all of the people at the party was exactly 66.74 years. If the average age of the men was exactly 69.74 years, which of the following was closest to the average age, in years, of the women?

(A) 61.24
(B) 63.74
(C) 64.24
(D) 64.74
(E) 69.24

The average age of the men is exactly three years more than the average age of the whole group, which got me to thinking . . .

These numbers are horrid for calculating. And although prompt asks for "closest to," the answer choices aren't far enough apart to estimate, IMO.

1. Use the group mean and the men's mean to find the weight (total number of years' difference from mean) of the men as a group

Whole group mean age is 66.74, and male age mean is 69.74.

Men's individual deviation from the mean is 69.74 - 66.74 = +3

There are 22 men, each is +3 away from the mean.

The sum of each man's deviation is +3 * 22 = +66.

2. Women as a group must balance out men

By definition of group mean, the women as a group must "balance out" this total of + 66.

Or, the sum of the positive differences from the mean (the men) must equal the sum of the negative differences from the mean (which must be the women's).

If you think about a scale with two plates, where men as a group are all on one plate, that group of men has a total weight.

The mean is a balance point.

The women as a group, on the other plate, must equal the absolute value of the men's total weight in order for the scale plates to "level" or balance each other out, such that there is a mean, i.e., the scale's balancing point.

3. Women's individual difference from mean calculated by women's group difference from mean divided by number of women

The men are heavier than the mean; the sum of their deviations is, as noted, +66.

So the women's group total difference from the mean must be - 66.

There are 26 women. Each woman's individual difference from the group's mean is \(\frac{-66}{26}\) = - 2.538 -- > round up to - 2.54 to make next subtraction easier

4. Average age of each woman

Group mean of 66.74 - individual woman's difference from mean (-2.54) will yield average age of each woman.

66.74 - 2.54 = 64.20

Answer (C).

66/26 wasn't a whole lot of fun by hand, but it looked better than multiplication and addition among 22, 26, 66.74, and 69.74. :shock: I think I might have been right. Hope it helps.
_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver



For practice SC questions with official explanations that were posted and moderated by the SC Team,
go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
Intern
Intern
avatar
B
Joined: 10 Nov 2014
Posts: 7
A total of 22 men and 26 women were at a party. The average (arithmeti  [#permalink]

Show Tags

New post 02 Jul 2017, 05:48
22*69.74 + 26w = 66.74*48
w = (66.74*48 - 69.74*22)/26
= (69.74*48 -3*48 - 69.74*22)/26
= (69.74(26) - 3*48)/26
= 69.74 - 5.53
= 64.21
Approx 64.24
Option C
GMAT Club Bot
A total of 22 men and 26 women were at a party. The average (arithmeti   [#permalink] 02 Jul 2017, 05:48
Display posts from previous: Sort by

A total of 22 men and 26 women were at a party. The average (arithmeti

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.