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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]  25 Oct 2009, 03:59
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Difficulty:

35% (medium)

Question Stats:

51% (02:42) correct 48% (01:13) wrong based on 39 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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Re: F + S [#permalink]  25 Oct 2009, 15:53
1
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Expert's post
Economist wrote:
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.

S+F=42

(1) S>4F --> S>4*(42-F) --> S>33.6. Seniors can be 34, 35, ... not sufficient.
(2) F>7. F=8, 9, ... Clearly not sufficient to determine S.

(1)+(2) S>=34 and F>=8 --> Only one value satisfies S=34. Sufficient.

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Re: F + S [#permalink]  25 Oct 2009, 18:39
Agreed with above solution

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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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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
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
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
Re: There are 42 students in a group. If each student is either   [#permalink] 04 Dec 2013, 00:22
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