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

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Senior Manager
Joined: 25 Oct 2008
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There are 42 students in a group. If each student is either  [#permalink]

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Updated on: 22 Apr 2014, 02:29
1
7
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:52) correct 39% (01:49) wrong based on 186 sessions

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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.

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http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902

Originally posted by tejal777 on 29 Sep 2009, 19:07.
Last edited by Bunuel on 22 Apr 2014, 02:29, edited 1 time in total.
Edited the question and added the OA.
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Re: freshmen or a senior  [#permalink]

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29 Sep 2009, 19:14
1
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

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25 Oct 2009, 16:53
2
1
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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25 Oct 2009, 19:52
I got C too. solution F=8 and S=34 is the only possibility from S1 and S2
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Re: freshmen or a senior  [#permalink]

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23 Apr 2011, 03:23
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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Re: freshmen or a senior  [#permalink]

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23 Apr 2011, 07:38
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.

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Re: freshmen or a senior  [#permalink]

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23 Apr 2011, 07:52
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

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Re: freshmen or a senior  [#permalink]

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23 Apr 2011, 09:33
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]

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03 Dec 2013, 22:22
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]

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04 Dec 2013, 01:15
1
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]

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04 Dec 2013, 01:22
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
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Re: There are 42 students in a group. If each student is either  [#permalink]

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26 Jan 2016, 22:42
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

In the original condition, there are 2 variables(f,s) and 1 equation(f+s=42), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), in s>4f, value of s is not unique and not sufficient.
For 2), in f>7, value of s is also not unique and not sufficient. When 1) & 2), they become s>4f and f>7 → s+f>4f+7, 42>4f+7, 35>4f → 35/4=8.75>f. Since f>7, in 8.75>f>7, f=8, s=34, which is unique and sufficient.

--> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: There are 42 students in a group. If each student is either  [#permalink]

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23 Dec 2018, 12:23
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Re: There are 42 students in a group. If each student is either   [#permalink] 23 Dec 2018, 12:23
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