Currently, y percent of the members on the finance committee

Question

Currently, y percent of the members on the finance committee are women and next month, z percent of the men on the finance committee will resign. If no other personnel changes occur, then after the resignations next month, the men who remain on the finance committee will represent what percent of the total finance committee members?

A.  \frac{100(100 - z)(100 - y)}{100^2 - z(100 - y)}

B.  \frac{(100 - z)(100 - y)}{100}

C.  (100 - z)(100 - y)

D.  \frac{zy}{100} - z

E.  \frac{z(100 - y)}{100}

KarishmaB · Accepted Answer

Yes, number plugging is the best choice here though I would take much easier numbers to reduce the time taken. Almost no calculations will be involved.

e.g. Say 50% are women i.e. y = 50 and say 100% of men will resign i.e. z = 100 so the correct option should give me 0. I see that z = 100 is not a problem because you don't have z - 100 anywhere in the denominators.
(A), (B) and (C) have z - 100 in the numerator so they will give us 0. (D) and (E) will not. So I will only worry about (A), (B) and (C).

Now say z = 50% i.e. the remaining men will be 25/75 = 1/3. Put z = 50 and y = 50 in (B) and (C) since they are simpler and you can just see what you will get without any calculations. Neither gives 33.33. Obviously, (A) will be the correct answer. You don't even need to plug in to check.

Answer (A)

Answer (A)

jaynayak · Answer

For these questions..... I find it better to take some values for y and z

for example.
Let total finance commitee members = 100
Let y = 20 and z = 5

hence men left = 80 - 4 = 76

Percent = 7600/96

Now lets plug in values in the choices. 
A = 100 * 95*80/10000 - 400
 = 100 * 95*80/9600
 = 7600/96

ps_dahiya · Answer

A

Current month:
Let total = 100
No. of females = y
No. of males = 100-y

Next month:
No of females = y
No of males = (100-y)*(100-z)/100
Total = y + (100-y)*(100-z)/100
 = (100y + 100^2 - 100y -100z+yz)/100
 =  /100

Percentage of males =   /  /100
i.e (100)(100 â€“ z)(100 â€“ y)/100^2 â€“ z(100 â€“ y)

Professor · Answer

w = y
m = 100 - y
total = 100 
m after z = (100 - y) -   = (100-z)(100-y)/100
m (after z) as a % of total =  /  x  

after solviing for y and z: m (after z) as a % of total =  / 

its A. imo, plugging-in is best for such a tedious calculation.

heman · Answer

Ps: How are you getting 100-z/100 when Q says z% of the men. Wouldnt it be (100-y)*z/100

Heman

Path · Answer

z pct men left, so the number of remaining men is 100-z pct of women.

ChrisLele · Answer

Hi, I know this is an ancient thread :-D

but was just replying in response to one of Magoosh's users who had asked me to take a look. The responses above are fine (check out ps-dahiya's). The thing with this problem is the algebraic solution is time-consuming and unwieldy. It is not that the users are missing a more elegant algebraic solution. The take away from a question such as this one - esp., if you want to answer it in under 2 minutes - is to plug in. @Jaynayak shows how to do so in his post. Hope that helps

.

jlgdr · Answer

Let's say that there are a total of 100 members
Let's also say that y = 50
So there are 50 men
Now z = 10 so 45 men are left
(45/95)*100 = 9/19 *100 = 900/19

Now let's plug answer choices
Target 900/19
Inputs
y=50
z=10

Only A gives the correct answer

Hope it helps
Cheers!
J

Raihanuddin · Answer

Number Plug has worked very quickly.
Let Total =100, Y= 50 and Z = 10. So New no. of men = .90*50 =45, New no. of total =100-5 =95 
Percent = (45/95)*100 = 900/19. Plug the y=50 and z= 10.
Remember, first plug in easy option. You will immediately find that in B, C, D and E you are not getting 19 in denominator. Ans-A

truongynhi · Answer

Hi Karishma,

I tried plugging numbers for option A, but somehow I cannot get 1/3.

\frac{{100*(100-50)*(100-50)}}{{100*100-50*(100-50)}}=\frac{{100*50*50}}{{100^2-50^2}}=\frac{{100*50*50}}{{50*150}}=\frac{5000}{150}

Could you please point out what is wrong with the above calculation?
Thank you very much!
Nhi

Raihanuddin · Answer

You can look at my solution

Number Plug has worked very quickly.
Let Total =100, Y= 50 and Z = 10. So New no. of men = .90*50 =45, New no. of total =100-5 =95 
Percent = (45/95)*100 = 900/19. Plug the y=50 and z= 10.
 
Remember, first plug the numbers in easy option. You will immediately find that in B, C, D and E you are not getting 19 in the denominator. Ans-A

truongynhi · Answer

Hi Raihanuddin,
Thank you for the prompt reply. But you didn't address my question. I understood the plugging method and knew that B, C, D, and E are wrong. I am asking about the arithmetic operation when plugging z=y=50 into option A.

chinelj · Answer

I'm sure there is an obvious answer to this but why did you subtract by 4 and not 5

KarishmaB · Answer

The question says "z percent of the men will resign."
If there are 80 men (assuming 20% are women and total employees are 100), then 5% of 80 is 4. That is why you subtract 4.

brandon7 · Answer

Can someone help me out why I am being such an idiot here? I can calculate the denominator but I get a slightly different answer for the numerator. Obviously I am missing something here, but I can't seem to figure it out.

Let's say:

T=Total
Y=W=Women
M=Men
Z=Men resigning

The # of men left over after men have resigned=
((100-y)/100) * T *((100-z)/100). I.e. (% of Men * Total)=# of Men * (% of Men Resigning).

The denominator= Women + men who haven't signed=
y/100*T + ((100-y)/100) * T *((100-z)/100)

Thus when I reduce this I get:
1. ((T)(100-y)(100-z))/100^2)/(((100*Y*T)/100^2)+((T)(100-y)(100-z))/100^2))

2. ((T)(100-y)(100-z))/100^2) / (((100*Y*T)+((100-y)(100-z)(t)))/100^2

3. ((T)(100-y)(100-z))/100^2) * 100^2/ (t)(100^2-z(100-y))

4. (100-y)(100-z))/(100^2-z(100-y))

What am I missing? Thanks!

KarishmaB · Answer

When you convert something into a percentage, you multiply by 100. Say, 2 is what percent of 4?
2/4 * 100 = 50
So 2 is 50% of 4.

I think you have missed multiplying by 100 at the end.

KarishmaB · Answer

When you convert something into a percentage, you multiply by 100. Say, 2 is what percent of 4?
2/4 * 100 = 50
So 2 is 50% of 4.

I think you have missed multiplying by 100 at the end.

pjthug · Answer

Here's an easier number, how about 0?

If there are zero percent women, and zero percent men that leave, you know that the answer you are looking for is 100. (Since no women are part of the set, and no men leave, you should have 100 percent men). Only A and B result in 100 when plugged in. Now use some logic to weed out answer B, let's pretend z=1 (one percent men leave) but still y=0 (no women). B would give us 99 percent men, which is false since it is still ALL men (even if some leave). Therefore, you are left with A.

Shrish_nayak · Answer

Hello Karishma,

Unfortunately, I am not getting the correct answer. I tried the below:

total = 20 people
women = 10 men=10 z%=10

so 10*10/100=1 hence remaining men = 9

total is 9/19*100 = 900/19

A. 100(100−10)(100−10)
 -------------------------- = 100*90*90/10000-900= 810000/9100 = 8100/91 
 100^2−10(100−10)

Can you help me where did I go wrong with this one?  VeritasPrepKarishma

Best Regards,
Shrish

Currently, y percent of the members on the finance committee

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Currently, y percent of the members on the finance committee

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