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

 It is currently 18 Oct 2019, 06:56

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

There are 750 male and female participants in a meeting. Half the fema

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453
There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

19 Aug 2018, 10:02
00:00

Difficulty:

25% (medium)

Question Stats:

82% (02:39) correct 18% (02:51) wrong based on 141 sessions

HideShow timer Statistics

There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

_________________
Director
Joined: 20 Feb 2015
Posts: 762
Concentration: Strategy, General Management
Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

19 Aug 2018, 10:07
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

m+f=750 -----1
f/2 + m/4 = democrats
750/3= democrats
2f+m=1000 ------2
subtracting 1 from 2
f=250
f who are democrats = f/2 = 125
Intern
Joined: 24 Aug 2018
Posts: 1
Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 07:03
sorry but i didn't get the explanation!
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4009
Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 07:31
1
Top Contributor
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

There are 750 male and female participants in a meeting.
Let M = the number of males
Let F = the number of females
So, we can write: F + M = 750

One-third of all the participants are Democrats.
1/3 of 750 = 250
So, there are 250 Democrats in TOTAL

Half the female participants and one-quarter of the male participants are Democrats
(# of female Democrats) + (# of male Democrats) = TOTAL number of Democrats
So, we can write: (1/2)F + (1/4)M = 250
To eliminate the fractions, let's multiply both sides by 4 to get: 2F + M = 1000

How many of the Democrats are female?
2F + M = 1000
F + M = 750
Subtract the bottom equation from the top equation to get: F = 250
So, there are 250 females, and we're told that 1/2 of them are Democrats
1/2 of 250 = 125

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
VP
Joined: 09 Mar 2016
Posts: 1230
There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 07:54
FAVEROL wrote:
sorry but i didn't get the explanation!

FAVEROL let me explain

let number of males be M
let number of females be F

$$\frac{1}{4}$$M = democrate males
$$\frac{1}{2}$$F = democrate females
Total number of democrates $$\frac{1}{3}*750 = 250$$

hence --- >

$$\frac{1}{4}$$M +$$\frac{1}{2}$$F = $$250$$

$$\frac{1}{2}$$F*$$250 = 125$$
So the Rest Part $$\frac{1}{4}= 125$$ its number of male democrats

So number of female democrates is $$125$$

Total number of females 250
Total number of males 500

Happy Studying

pushpitkc is my approach correct ? thanks!
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4771
Location: India
GPA: 3.5
Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 08:14
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

Let total no of Female participants be 2f and total no of males be 4m and $$2f + 4m = 750$$

Now, $$f + m = 250$$

Plug in $$f = 250 - m$$ in the first equation and check -

So, $$2( 250 - m) + 4m = 750$$

Or,$$500 - 2m + 4m = 750$$

Or,$$2m = 250$$

Or, $$m = 125$$

Now, $$f + m = 250$$

So, $$f + 125 = 250$$

Hence, f = 125 , Answer must 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 PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 10:57
1
dave13 wrote:
FAVEROL wrote:
sorry but i didn't get the explanation!

FAVEROL let me explain

let number of males be M
let number of females be F

$$\frac{1}{4}$$M = democrate males
$$\frac{1}{2}$$F = democrate females
Total number of democrates $$\frac{1}{3}*750 = 250$$

hence --- >

$$\frac{1}{4}$$M +$$\frac{1}{2}$$F = $$250$$

$$\frac{1}{2}$$F*$$250 = 125$$
So the Rest Part $$\frac{1}{4}= 125$$ its number of male democrats

So number of female democrates is $$125$$

Total number of females 250
Total number of males 500

Happy Studying

pushpitkc is my approach correct ? thanks!

Hey dave13

Just one thing - how did you go from $$\frac{1}{4}$$M +$$\frac{1}{2}$$F = $$250$$ -> $$\frac{1}{2}$$F*$$250 = 125$$

Your answer is absolutely correct - but this part if not so clear to me!

I'm thrilled that you are getting a lot of questions correct now but just want to be sure it is for the right reason
_________________
You've got what it takes, but it will take everything you've got
VP
Joined: 09 Mar 2016
Posts: 1230
There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 12:09
pushpitkc wrote:
dave13 wrote:
FAVEROL wrote:
sorry but i didn't get the explanation!

FAVEROL let me explain

let number of males be M
let number of females be F

$$\frac{1}{4}$$M = democrate males
$$\frac{1}{2}$$F = democrate females
Total number of democrates $$\frac{1}{3}*750 = 250$$

hence --- >

$$\frac{1}{4}$$M +$$\frac{1}{2}$$F = $$250$$

$$\frac{1}{2}$$F*$$250 = 125$$
So the Rest Part $$\frac{1}{4}= 125$$ its number of male democrats

So number of female democrates is $$125$$

Total number of females 250
Total number of males 500

Happy Studying

pushpitkc is my approach correct ? thanks!

Hey dave13

Just one thing - how did you go from $$\frac{1}{4}$$M +$$\frac{1}{2}$$F = $$250$$ -> $$\frac{1}{2}$$F*$$250 = 125$$

Your answer is absolutely correct - but this part if not so clear to me!

I'm thrilled that you are getting a lot of questions correct now but just want to be sure it is for the right reason

Hey pushpitkc

lemme explain my logic

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

I know that $$\frac{1}{4}$$M +$$\frac{1}{2}$$F = $$250$$

So from 250 $$\frac{1}{2}$$ will be female democrates and $$\frac{1}{4}$$ will be male democrates

Say i will make this step $$\frac{1}{4}$$ *250 = so i get 62 which doesnt work at all looking at answer choices

But if i multiply $$\frac{1}{2}$$* 250 i get 125 --- > that means $$\frac{1}{2}$$f equals 125 and the rest 250-125 =125 logically equals 1/4 of total male demacrates from total number of males

because if 125 is 1/4 i.e. 0.25 % the total number of males is 500

same logic if 125 equals 1/2 of number i.e. 0.50 the total number of females is 250

250+500 = 750

Director
Joined: 20 Feb 2015
Posts: 762
Concentration: Strategy, General Management
There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 13:09
FAVEROL wrote:
sorry but i didn't get the explanation!

Hello,

although you already have the explanation, the first three lines of my solution is nothing but the question stem ,rest just manipulation.
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

29 Aug 2018, 13:17
FAVEROL wrote:
sorry but i didn't get the explanation!

Here we have to take care of 2 distinctions.
1) participants
2) Democrats

To find :- #female Democrats=F/2,say F is #of female participants (Given half of the female participants are democrats )
Given :-
#participants=750=#male participants+#female participants or #male participants=750-#female participants–-----------(a)
#democrats=One-third of participants=750/3=250
Half of #female participants+one-fourth of male participants=#democrats=250----(b)
Since we need #female participants,so we have to substitute #male participants by a expression that relates to #female participants.(Expression (a) )

So expression(b) can be written as
#female participants/2+1/4*(750-#female participants)=250
Now the above expression is an algebra equation with 1 variable,so we can solve it.
F/2+750/4-F/4=250
F/2-F/4=250-750/4=250/4
Or. F/4=250/4
Multiply both sides by 2
F/2=125

Ans. (C)

Hope this helps.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

03 Sep 2018, 18:58
Bunuel wrote:
There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

We can let f = the number of females and m = the number males in the meeting. So we have:

f + m = 750

Since 1/3 of the participants are Democrats, 750/3 = 250 are Democrats. So we have:

½f + ¼m = 250

Since m = 750 - f, we have:

½f + ¼(750 - f) = 250

Multiplying the equation by 4, we have:

2f + 750 - f = 1000

f = 250

Since half the female participants are Democrats, there are 125 female Democrats.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com
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.

Non-Human User
Joined: 09 Sep 2013
Posts: 13257
Re: There are 750 male and female participants in a meeting. Half the fema  [#permalink]

Show Tags

23 Sep 2019, 13:22
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: There are 750 male and female participants in a meeting. Half the fema   [#permalink] 23 Sep 2019, 13:22
Display posts from previous: Sort by