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

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Currently, y percent of the members on the finance committee [#permalink]

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08 Aug 2006, 12:21
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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. $$\frac{z(100 - y)}{100}$$
[Reveal] Spoiler: OA

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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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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17346 [5], given: 232 SVP Joined: 30 Mar 2006 Posts: 1728 Kudos [?]: 98 [4], given: 0 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 11 Aug 2006, 03:04 4 This post received KUDOS 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 Kudos [?]: 98 [4], given: 0 CEO Joined: 20 Nov 2005 Posts: 2892 Kudos [?]: 323 [1], given: 0 Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 08 Aug 2006, 12:39 1 This post received KUDOS 2 This post was BOOKMARKED 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) _________________ SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008 Kudos [?]: 323 [1], given: 0 VP Joined: 29 Dec 2005 Posts: 1338 Kudos [?]: 69 [1], given: 0 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 08 Aug 2006, 13:28 1 This post received KUDOS 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. Kudos [?]: 69 [1], given: 0 Magoosh GMAT Instructor Joined: 28 Nov 2011 Posts: 303 Kudos [?]: 1226 [1], given: 2 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 18 Apr 2012, 15:46 1 This post received KUDOS 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 . _________________ Christopher Lele Magoosh Test Prep Kudos [?]: 1226 [1], given: 2 Current Student Joined: 06 Sep 2013 Posts: 1978 Kudos [?]: 719 [1], given: 355 Concentration: Finance Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 16 Jan 2014, 16:00 1 This post received KUDOS 1 This post was BOOKMARKED 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 Kudos [?]: 719 [1], given: 355 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7674 Kudos [?]: 17346 [1], given: 232 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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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

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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.

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

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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

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

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

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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.

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

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

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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.

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

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

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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.

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

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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

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

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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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17346 [0], given: 232 Intern Joined: 09 Mar 2017 Posts: 36 Kudos [?]: 2 [0], given: 23 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 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! Kudos [?]: 2 [0], given: 23 Intern Joined: 09 Mar 2017 Posts: 36 Kudos [?]: 2 [0], given: 23 Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 04 Aug 2017, 09:18 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! Bump, does anyone know? Kudos [?]: 2 [0], given: 23 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7674 Kudos [?]: 17346 [0], given: 232 Location: Pune, India Re: Currently, y percent of the members on the finance committee [#permalink] ### Show Tags 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Currently, y percent of the members on the finance committee   [#permalink] 05 Aug 2017, 02:54

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