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

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

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New post 29 Sep 2009, 19:07
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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.
[Reveal] Spoiler: OA

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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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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

SO C is the Answer
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Re: freshmen or a senior [#permalink]

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New post 29 Sep 2009, 19:29
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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Re: freshmen or a senior [#permalink]

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New post 29 Sep 2009, 21:28
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
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Re: freshmen or a senior [#permalink]

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New post 03 Oct 2009, 00:54
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.
Answer is C.
Because if F=9 and S>4F...this will make the number of students larger than 42.

I hope I made sense.
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Re: F + S [#permalink]

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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?

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.

Answer: C.
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Re: F + S [#permalink]

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New post 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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New post 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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New post 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.

Answer is C.
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Re: freshmen or a senior [#permalink]

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New post 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


Answer C
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Re: freshmen or a senior [#permalink]

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New post 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

Answer - C
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Re: There are 42 students in a group. If each student is either [#permalink]

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New post 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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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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New post 04 Dec 2013, 01:22
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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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New post 26 Jan 2016, 22:42
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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.
Therefore, the answer is C.


--> 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] 26 Jan 2016, 22:42
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