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

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VP
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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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Difficulty:

75% (hard)

Question Stats:

58% (03:52) correct 42% (02:14) wrong based on 377 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. (100)(100 - z)(100 - y)/(100^2 - z(100 - y))
B. (100 - z)(100 - y)/100
C. (100 - z)(100 - y)
D. zy/100 - z
E. z(100 - y)/100
[Reveal] Spoiler: OA
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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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VP
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08 Aug 2006, 13:28
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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.
VP
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08 Aug 2006, 13:30
Professor wrote:
its A. imo, plugging-in is best for such a tedious calculation.

agree... but took me 2.5 min to do so
VP
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08 Aug 2006, 13:40
Going with A...
tedious calculation for me... took more than 2 mins for sure.

At the end looked at the choices and picked A based on how it looked compared to my results.
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08 Aug 2006, 16:08
Arrived safely at (A), but I agree that clalculations are tedious...
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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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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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11 Aug 2006, 03:04
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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
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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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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
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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
4
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Expert's post
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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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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14 Sep 2015, 11:42
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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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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.
Re: Currently, y percent of the members on the finance committee   [#permalink] 02 Mar 2016, 23:30
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