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A business school event invites all of its graduate and unde

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A business school event invites all of its graduate and unde [#permalink]

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New post 27 May 2014, 19:01
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A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

A) 18
B) 27
C) 36
D) 72
E) 180

I tried to solve using a Double Set Matrix:

------------------Male--------Female---------Total
Graduate 7x 2x 9x
Under Graduate - - (1/6)100
Total 30 70 100

Is it correct here to take the Total as 100 since it is mentioned that females constitute 70% of the group or should the total be an unknown x? Thanks for your help.

Regards,
Sri
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 May 2014, 01:08, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Number of graduates [#permalink]

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gmattesttaker2 wrote:
Hello,

Can you please assist with this:

A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

A) 18
B) 27
C) 36
D) 72
E) 180


OA:
[Reveal] Spoiler:
B



I tried to solve using a Double Set Matrix:

------------------Male--------Female---------Total
Graduate 7x 2x 9x
Under Graduate - - (1/6)100
Total 30 70 100

Is it correct here to take the Total as 100 since it is mentioned that females constitute 70% of the group or should the total be an unknown x? Thanks for your help.

Regards,
Sri



Here is how you can use the double set matrix.

...................Male...............Female..............Total
Graduate .......7x..............
UnderGrad......2x......
Total.............9x

Female students make up 70% of the group and so male students make up 30% of the group.
9x = (30/100)*Total
Total = 30x (we got the total number of students in terms of x)

...................Male...............Female..............Total
Graduate .......7x................
UnderGrad......2x......
Total.............9x...................21x.................30x

Undergrad students make 1/6 of the group i.e. (1/6)*30x = 5x

...................Male...............Female..............Total
Graduate .......7x...................18x
UnderGrad......2x...................3x....................5x
Total.............9x...................21x.................30x

So undergrad females must be 3x and grad females must be 18x.

Number of Grad females must be a multiple of 18.
27 is not a multiple of 18 so it cannot be the number of grad females. Answer (B)
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Re: Number of graduates [#permalink]

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New post 27 May 2014, 22:12
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gmattesttaker2 wrote:
Hello,

Can you please assist with this:

A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

A) 18
B) 27
C) 36
D) 72
E) 180


OA:
[Reveal] Spoiler:
B



I tried to solve using a Double Set Matrix:

------------------Male--------Female---------Total
Graduate 7x 2x 9x
Under Graduate - - (1/6)100
Total 30 70 100

Is it correct here to take the Total as 100 since it is mentioned that females constitute 70% of the group or should the total be an unknown x? Thanks for your help.

Regards,
Sri


If you do assume the total to be 100, you will get fractions at places since the total is 30x. So the total must be a multiple of 30. In such cases, it is best to get everything in a single variable.
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Re: Number of graduates [#permalink]

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New post 31 May 2014, 20:28
VeritasPrepKarishma wrote:
gmattesttaker2 wrote:
Hello,

Can you please assist with this:

A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

A) 18
B) 27
C) 36
D) 72
E) 180


OA:
[Reveal] Spoiler:
B



I tried to solve using a Double Set Matrix:

------------------Male--------Female---------Total
Graduate 7x 2x 9x
Under Graduate - - (1/6)100
Total 30 70 100

Is it correct here to take the Total as 100 since it is mentioned that females constitute 70% of the group or should the total be an unknown x? Thanks for your help.

Regards,
Sri



Here is how you can use the double set matrix.

...................Male...............Female..............Total
Graduate .......7x..............
UnderGrad......2x......
Total.............9x

Female students make up 70% of the group and so male students make up 30% of the group.
9x = (30/100)*Total
Total = 30x (we got the total number of students in terms of x)

...................Male...............Female..............Total
Graduate .......7x................
UnderGrad......2x......
Total.............9x...................21x.................30x

Undergrad students make 1/6 of the group i.e. (1/6)*30x = 5x

...................Male...............Female..............Total
Graduate .......7x...................18x
UnderGrad......2x...................3x....................5x
Total.............9x...................21x.................30x

So undergrad females must be 3x and grad females must be 18x.

Number of Grad females must be a multiple of 18.
27 is not a multiple of 18 so it cannot be the number of grad females. Answer (B)


Hello Karishma,

Thank you very much for the excellent explanation.

Best Regards,
Sri

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Re: A business school event invites all of its graduate and unde [#permalink]

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New post 09 Jun 2014, 09:10
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A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

I solved this question in a different way and stuck:

I considered total students = X

Females 70% of X
Males 30% of X

Male grad to undergrad ratio = 7:2

Therefore male undergrads in X = 2/9 * 3/10 X

= 1/15 * X

1/6 of the group are undergrad, i.e 1/6 * X

Female undergrad = 1/6 * X - 1/15 * X = X/10

Thus, Female grad = (7/10 * X )- X/10 = 3/5 * X

As per my solution Female grad number must be divisible by 3 and all choices are divisible by 3. I am not able to identify any error in my approach.. please help to identify mistake in my solution.
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Re: A business school event invites all of its graduate and unde [#permalink]

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New post 09 Jun 2014, 21:24
PiyushK wrote:
A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

I solved this question in a different way and stuck:

I considered total students = X

Females 70% of X
Males 30% of X

Male grad to undergrad ratio = 7:2

Therefore male undergrads in X = 2/9 * 3/10 X

= 1/15 * X

1/6 of the group are undergrad, i.e 1/6 * X

Female undergrad = 1/6 * X - 1/15 * X = X/10

Thus, Female grad = (7/10 * X )- X/10 = 3/5 * X

As per my solution Female grad number must be divisible by 3 and all choices are divisible by 3. I am not able to identify any error in my approach.. please help to identify mistake in my solution.



You get that Number of female grads is (3/5)*X.
Note that X needs to be divisible by 10 since number of female is 7/10*X, number of males is 3/10*X etc.
So X should be a multiple of 2. Since number of female grads is (3/5)*X, number of female grads should be a multiple of 2 too. So 27 is not possible.
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Re: A business school event invites all of its graduate and unde [#permalink]

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New post 09 Jun 2014, 22:21
I tried it this way.

MG: MUG => 7/9 : 2/9
M:F => 3/10 : 7/10
UG:G => 1/6 : 5/6

If we take LCM of the denominators i.e. 9,10 and 6, we get 90.

Wouldnt this mean that this group HAS TO HAVE the total number of students in multiples of 90.
If so then FG would be 54/90 or 3/5 or 60% of the group to be Female Grads.
Only 27 is the number which is not a multiple of 6, hence thats the correct answer.

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Re: A business school event invites all of its graduate and unde [#permalink]

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Re: A business school event invites all of its graduate and unde [#permalink]

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New post 28 Mar 2016, 14:08
The ratio of female grad to female undergrad is 6:1. The answer will not be divisble by 6. So, 27-B.

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Re: A business school event invites all of its graduate and unde [#permalink]

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New post 01 Apr 2016, 22:52
VeritasPrepKarishma wrote:
gmattesttaker2 wrote:
Hello,

Can you please assist with this:

A business school event invites all of its graduate and undergraduate students to attend. Of the students who attend, male graduate students outnumber male undergraduates by a ratio of 7 to 2, and females constitute 70% of the group. If undergraduate students make up 1/6 of the group, which of the following CANNOT represent the number of female graduate students at the event?

A) 18
B) 27
C) 36
D) 72
E) 180


OA:
[Reveal] Spoiler:
B



I tried to solve using a Double Set Matrix:

------------------Male--------Female---------Total
Graduate 7x 2x 9x
Under Graduate - - (1/6)100
Total 30 70 100

Is it correct here to take the Total as 100 since it is mentioned that females constitute 70% of the group or should the total be an unknown x? Thanks for your help.

Regards,
Sri



Here is how you can use the double set matrix.

...................Male...............Female..............Total
Graduate .......7x..............
UnderGrad......2x......
Total.............9x

Female students make up 70% of the group and so male students make up 30% of the group.
9x = (30/100)*Total
Total = 30x (we got the total number of students in terms of x)

...................Male...............Female..............Total
Graduate .......7x................
UnderGrad......2x......
Total.............9x...................21x.................30x

Undergrad students make 1/6 of the group i.e. (1/6)*30x = 5x

...................Male...............Female..............Total
Graduate .......7x...................18x
UnderGrad......2x...................3x....................5x
Total.............9x...................21x.................30x

So undergrad females must be 3x and grad females must be 18x.

Number of Grad females must be a multiple of 18.
27 is not a multiple of 18 so it cannot be the number of grad females. Answer (B)


I really like your posts Karishma, superb explanations.
My only concern there are times I don't know how to approach a question, but after reading your explanations it makes perfect sense. How do i work on this?

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Re: A business school event invites all of its graduate and unde [#permalink]

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Re: A business school event invites all of its graduate and unde [#permalink]

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New post 17 Sep 2017, 00:12
Given\(\frac{Male Grad}{Male Undergard} =\frac{MG}{MUG}=\frac{7}{2}\)

=> MG = 7x and MUG =2x

No. of females = F = 70 % of total = 0.7T
=> No. of males = M = T - 0.7T = 0.3T

=> No. of Male Grad + No. of Male Undergrad = Total Males => MG+MUG = M => 7x+2x =0.3T => 9x = 0.3T => T = 30x

Total Undergrad = UG = 1/6th of total = \(\frac{T}{6}\) =\(\frac{30x}{6}\) =5x

=> Male undergrad + Female undergrad = Total Undergrad students => MUG + FUG = UG => 2x+FUG = 5x => FUG = 3x

=> Female Undergrad + Female Grad = Total Female students = > FUG + FG = F => 3x+FG = 0.7 T = 0.7*30x => FG = 21x-3x = 18x

So number of FG need to be a multiple of 18. Wrong out option which is not a multiple of 18.

Answer: B

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Re: A business school event invites all of its graduate and unde   [#permalink] 17 Sep 2017, 00:12
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