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

Question

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

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

CounterSniper · Answer

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

FAVEROL · Answer

sorry but i didn't get the explanation!

BrentGMATPrepNow · Answer

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?  
We already know:
 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

Answer: C

Cheers,
Brent

dave13 · Answer

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!

Abhishek009 · Answer

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)

pushpitkc · Answer

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

dave13 · Answer

Hey pushpitkc

lemme explain my logic

look at answer choices (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

CounterSniper · Answer

Hello,

although you already have the explanation, the first three lines of my solution is nothing but the question stem ,rest just manipulation.

PKN · Answer

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.

JeffTargetTestPrep · Answer

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.

Answer: C

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