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# Currently, y percent of the members on the finance committee

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VP
Joined: 14 May 2006
Posts: 1380
Currently, y percent of the members on the finance committee [#permalink]

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08 Aug 2006, 12:21
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85% (hard)

Question Stats:

60% (02:34) correct 40% (02:14) wrong based on 541 sessions

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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. $$\frac{z(100 - y)}{100}$$
CEO
Joined: 20 Nov 2005
Posts: 2852
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Re: Currently, y percent of the members on the finance committee [#permalink]

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08 Aug 2006, 12:39
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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
= [100^2 - z(100-y)]/100

Percentage of males = [100 * (100-y)*(100-z)/100] / [100^2 - z(100-y)]/100
i.e (100)(100 â€“ z)(100 â€“ y)/100^2 â€“ z(100 â€“ y)
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
Joined: 29 Dec 2005
Posts: 1330
Re: Currently, y percent of the members on the finance committee [#permalink]

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08 Aug 2006, 13:28
1
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w = y
m = 100 - y
total = 100
m after z = (100 - y) - [z (100- y)/100] = (100-z)(100-y)/100
m (after z) as a % of total = [(100-z)(100-y)/100]/[{(100-y)(100-z)/100} + y] x [100]

after solviing for y and z: m (after z) as a % of total = [100 (100-z)(100-y)]/[(100^2 - z (100-y)]

its A. imo, plugging-in is best for such a tedious calculation.
Manager
Joined: 20 Mar 2006
Posts: 200
Re: Currently, y percent of the members on the finance committee [#permalink]

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09 Aug 2006, 17:54
ps_dahiya wrote:
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
= [100^2 - z(100-y)]/100

Percentage of males = [100 * (100-y)*(100-z)/100] / [100^2 - z(100-y)]/100
i.e (100)(100 â€“ z)(100 â€“ y)/100^2 â€“ z(100 â€“ y)

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

Heman
Manager
Joined: 07 Aug 2005
Posts: 117
Re: Currently, y percent of the members on the finance committee [#permalink]

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09 Aug 2006, 20:41
heman wrote:
ps_dahiya wrote:
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
= [100^2 - z(100-y)]/100

Percentage of males = [100 * (100-y)*(100-z)/100] / [100^2 - z(100-y)]/100
i.e (100)(100 â€“ z)(100 â€“ y)/100^2 â€“ z(100 â€“ y)

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

Heman

z pct men left, so the number of remaining men is 100-z pct of women.
SVP
Joined: 30 Mar 2006
Posts: 1711
Re: Currently, y percent of the members on the finance committee [#permalink]

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11 Aug 2006, 03:04
4
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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
Magoosh GMAT Instructor
Joined: 28 Nov 2011
Posts: 303
Re: Currently, y percent of the members on the finance committee [#permalink]

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18 Apr 2012, 15:46
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Expert's post
Hi, I know this is an ancient thread 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 .
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Christopher Lele
Magoosh Test Prep

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Joined: 06 Sep 2013
Posts: 1891
Concentration: Finance
Re: Currently, y percent of the members on the finance committee [#permalink]

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16 Jan 2014, 16:00
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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

Target 900/19
Inputs
y=50
z=10

Only A gives the correct answer

Hope it helps
Cheers!
J
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8079
Location: Pune, India
Re: Currently, y percent of the members on the finance committee [#permalink]

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16 Jan 2014, 20:40
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Expert's post
1
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jlgdr wrote:
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

Target 900/19
Inputs
y=50
z=10

Only A gives the correct answer

Hope it helps
Cheers!
J

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.

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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 11 Sep 2013 Posts: 149 Concentration: Finance, Finance Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 24 Aug 2014, 12:33 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 Intern Joined: 05 Jun 2015 Posts: 25 Location: Viet Nam GMAT 1: 740 Q49 V41 GPA: 3.66 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 02 Mar 2016, 21:55 VeritasPrepKarishma wrote: 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) 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 Manager Joined: 11 Sep 2013 Posts: 149 Concentration: Finance, Finance Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 02 Mar 2016, 23:03 truongynhi wrote: VeritasPrepKarishma wrote: 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) 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 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 Intern Joined: 05 Jun 2015 Posts: 25 Location: Viet Nam GMAT 1: 740 Q49 V41 GPA: 3.66 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 02 Mar 2016, 23:30 Raihanuddin wrote: 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 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. Intern Joined: 09 Dec 2014 Posts: 5 WE: Information Technology (Health Care) Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 12 Apr 2017, 14:23 jaynayak wrote: 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 I'm sure there is an obvious answer to this but why did you subtract by 4 and not 5 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8079 Location: Pune, India Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 13 Apr 2017, 04:11 chinelj wrote: jaynayak wrote: 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 I'm sure there is an obvious answer to this but why did you subtract by 4 and not 5 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Posts: 40
Re: Currently, y percent of the members on the finance committee [#permalink]

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22 Jul 2017, 08:36
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!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8079
Location: Pune, India
Re: Currently, y percent of the members on the finance committee [#permalink]

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05 Aug 2017, 02:54
brandon7 wrote:
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!

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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8079 Location: Pune, India Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 05 Aug 2017, 03:14 1 This post received KUDOS Expert's post brandon7 wrote: 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! 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Joined: 12 Feb 2017
Posts: 3
Re: Currently, y percent of the members on the finance committee [#permalink]

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07 Aug 2017, 18:15
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.
Intern
Joined: 03 Apr 2017
Posts: 18
Currently, y percent of the members on the finance committee [#permalink]

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30 Dec 2017, 05:11
VeritasPrepKarishma wrote:
jlgdr wrote:
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

Target 900/19
Inputs
y=50
z=10

Only A gives the correct answer

Hope it helps
Cheers!
J

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.

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   [#permalink] 30 Dec 2017, 05:11

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