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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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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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New post 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 – z)(100 – y)/100^2 – z(100 – y)
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Re: Currently, y percent of the members on the finance committee [#permalink]

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New post 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.

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

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New post 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 – z)(100 – y)/100^2 – z(100 – 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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New post 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 – z)(100 – y)/100^2 – z(100 – 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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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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New post 18 Apr 2012, 15:46
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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 :).
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Re: Currently, y percent of the members on the finance committee [#permalink]

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New post 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

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 :)

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

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New post 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

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 :)


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

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New post 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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New post 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

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

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New post 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

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

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

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New post 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!

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

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New post 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?

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

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

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New post 05 Aug 2017, 03:14
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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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Re: Currently, y percent of the members on the finance committee   [#permalink] 05 Aug 2017, 03:14

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