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# There are 42 students in a group. If each student is either

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Director
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There are 42 students in a group. If each student is either [#permalink]  29 Sep 2009, 18:07
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:16) correct 47% (01:13) wrong based on 42 sessions
There are 42 students in a group. If each student is either a freshmen or a senior, how many of the students are seniors?

(1) The group has more than four times as many seniors as it has freshmen.

(2) The group has more than 7 freshmen.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Apr 2014, 01:29, edited 1 time in total.
Edited the question and added the OA.
Manager
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Re: freshmen or a senior [#permalink]  29 Sep 2009, 18:14
1
KUDOS
There are 42 students in a group. If each student is either a freshmen or a senior, how many of the students are seniors?

(1) The group has more than four times as many seniors as it has freshmen.

(2) The group has more than 7 freshmen.

from 1:

the total sudents would be f*5 + x=42

from 2:
Substituting a value more than 7(only 8 satisfies)
will give a solution

Director
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Re: freshmen or a senior [#permalink]  29 Sep 2009, 18:29
Not clear.
If x=freshman,then from stmt 1 we get seniors=5x,6x,7x,8x...as more than four times is mentioned.

Stmt 2 insuff..

Combining,
6x=42, x=7 stmt 2 says more than 7 freshmen so not poss.
7x=42,x=6 which is again not greater than 7

I am messing it up..could u pls pt out my mistake?
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Senior Manager
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Re: freshmen or a senior [#permalink]  29 Sep 2009, 20:28
tejal777 wrote:
Not clear.
If x=freshman,then from stmt 1 we get seniors=5x,6x,7x,8x...as more than four times is mentioned.
Stmt 2 insuff..

Statement 1:
S = 4*F + C

tejal777 wrote:
Combining,
6x=42, x=7 stmt 2 says more than 7 freshmen so not poss.
7x=42,x=6 which is again not greater than 7

I am messing it up..could u pls pt out my mistake?

Combining 1 and 2 we get
42 = 4*8 + C + 8, where C = 2
Intern
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Re: freshmen or a senior [#permalink]  02 Oct 2009, 23:54
Statement 1:Insufficient (easy to find out)
Statement 2:F>7 Insufficient again.

1&2 together
The only one situation that will comply with the two statments is:
F=8 and S=34.
Because if F=9 and S>4F...this will make the number of students larger than 42.

Math Expert
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Re: F + S [#permalink]  25 Oct 2009, 15:53
1
KUDOS
Expert's post
There are 42 students in a group. If each student is either a freshmen or a senior, how many of the students are seniors?

Given: S+F=42.
Question: S=?

(1) The group has more than four times as many seniors as it has freshmen --> $$S>4F$$ --> $$S>4*(42-S)$$ --> $$S>33.6$$. The number of seniors can be 34, 35, ... Not sufficient.

(2) The group has more than 7 freshmen --> $$F>7$$ --> $$42-S>7$$ --> $$S<35$$. Not sufficient.

(1)+(2) $$S>33.6$$ and $$S<35$$ --> $$S=34$$. Sufficient.

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Senior Manager
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Re: F + S [#permalink]  25 Oct 2009, 18:52
I got C too. solution F=8 and S=34 is the only possibility from S1 and S2
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Manager
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Re: freshmen or a senior [#permalink]  23 Apr 2011, 02:23
ST 1 - insufficent
st 2 - in suff
combing 1 & 2
we get only one value > 7 which is 8 that satisfy answer

hence c
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lets start again

Director
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Kudos [?]: 71 [0], given: 42

Re: freshmen or a senior [#permalink]  23 Apr 2011, 06:38
f + s =42.

1. Insufficient
s > 4f
s > 4(42-s)
s > 33.6
s >=34
s could be 34 ,35....

2. Insufficient.

we dont know anthing about s.

together , Sufficient
as s = 34 , f = 8 is the only combination that satisfies 1 and 2.

Manager
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Re: freshmen or a senior [#permalink]  23 Apr 2011, 06:52
Statement 1 - Insufficient... Many answers are possible
Statement 2 - Nothing can be derived from this

Both together - 35 & 7 is an option but from statement 2, more than 7
34 and 8 is possible (more than 4:1 and also 8)
33 and 9 is not possible as statement 1 is not satisfied

So only one answer when two statements considered together

SVP
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Kudos [?]: 345 [0], given: 36

Re: freshmen or a senior [#permalink]  23 Apr 2011, 08:33
x + y = 42

(1)

x > 4y

42 -y > 4y

y < 8.4

So, y = 8,7 etc.

x = 34, 35 etc.

Not Sufficient

(2)

y > 7

Not Sufficient

(1) and (2)

y = 8, x = 34

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Re: There are 42 students in a group. If each student is either [#permalink]  23 Nov 2013, 08:45
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Re: There are 42 students in a group. If each student is either [#permalink]  03 Dec 2013, 21:22
The translation of (1) killed me in this problem.
I thought it meant 4s > f. Can someone help me translate it to s > 4f?
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Re: There are 42 students in a group. If each student is either [#permalink]  04 Dec 2013, 00:15
1
KUDOS
TooLong150 wrote:
The translation of (1) killed me in this problem.
I thought it meant 4s > f. Can someone help me translate it to s > 4f?

The statement clearly states that "more than four times as many seniors as it has freshmen."
Lets forget more than part here and focus on four times as many seniors as it has freshmen.
This means S=4F
now more than part . incorporate > in place of =.
So S > 4F
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Re: There are 42 students in a group. If each student is either [#permalink]  04 Dec 2013, 00:22
2
KUDOS
C.

Statement 1:
s>4F

>4F+F = 42
F & S should be an integers.
So I found factors of 42 fitting to solve the equation .
Factors of 42 = 1,2,3,6,7,14,21,42.
So 5F + F = 42 => F=7 & S = 35
6F+F= 42 => F = 6 & S=36. and so on for other values. => Not sufficient.

Statement 2:
F>7.
Many values satisfy this condition such as F = 8 & S = 34; F=9 & S = 33 & so on =>Insufficient

Combine both :
F>7 and S>4F . F = 8 & S = 34

Hence C
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Re: There are 42 students in a group. If each student is either [#permalink]  21 Apr 2014, 07:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: There are 42 students in a group. If each student is either   [#permalink] 21 Apr 2014, 07:23
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