Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58261

A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
20 Oct 2015, 03:06
Question Stats:
72% (02:36) correct 28% (02:46) wrong based on 788 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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Retired Moderator
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
20 Oct 2015, 06:18
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: \(\frac{Weight 1}{Weight 2} = \frac{Average2Average}{AverageAverage1}\) For or example: \(\frac{26}{22} = \frac{3835}{35Average1}\) 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.




Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2401
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
20 Oct 2015, 03:43
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 :3835 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
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
20 Oct 2015, 07:09
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)..........(35x)............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: \(\frac{26}{22}=\frac{3}{(35x)}\) 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
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
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!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



CEO
Joined: 12 Sep 2015
Posts: 3990
Location: Canada

A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
Updated on: 06 Mar 2018, 10:49
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 womenAnd 26/48 = the proportion of menLet x = average age of the womenSo, 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
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
Joined: 01 Mar 2015
Posts: 69

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
21 Oct 2015, 04:54
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
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
19 Mar 2016, 11:41
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
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
04 May 2016, 09:55
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
_________________
5star 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
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4753
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
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
_________________



Manager
Joined: 18 Aug 2013
Posts: 121
Location: India
Concentration: Operations, Entrepreneurship
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
16 May 2016, 20:05
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
Joined: 17 Jun 2016
Posts: 500
Location: India
GMAT 1: 720 Q49 V39 GMAT 2: 710 Q50 V37
GPA: 3.65
WE: Engineering (Energy and Utilities)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
11 Aug 2016, 06:42
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 3835 = 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 = 352.5 = 32.5 Kudos if u like the method....



Manager
Joined: 30 Dec 2015
Posts: 82
GPA: 3.92
WE: Engineering (Aerospace and Defense)

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
09 Oct 2016, 16:02
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: [Womenavg: (w)]3538 \(\frac{26}{22} = \frac{3}{(35w)}\) \(w = 35  \frac{33}{13}\) 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
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
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: \(\frac{Weight 1}{Weight 2} = \frac{Average2Average}{AverageAverage1}\) For or example: \(\frac{26}{22} = \frac{3835}{35Average1}\) Solving for Average1 you will get exactly 32.46154. Answer D. Posted from my mobile device



Read Only User
Status: booyeh!
Joined: 26 May 2017
Posts: 15
Location: India
Concentration: Strategy, Marketing

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
17 May 2019, 20:50
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
Joined: 03 Aug 2017
Posts: 60

Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
Show Tags
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 womenAnd 26/48 = the proportion of menLet x = average age of the womenSo, 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 ?




Re: A total of 22 men and 26 women were at a party, and the average
[#permalink]
11 Oct 2019, 03:46






