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

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1
7 00:00

Difficulty:   55% (hard)

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

### HideShow timer Statistics 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.
Manager  Joined: 21 May 2009
Posts: 86
Re: freshmen or a senior  [#permalink]

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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

Math Expert V
Joined: 02 Sep 2009
Posts: 56260

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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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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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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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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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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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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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Manager  Joined: 10 Mar 2013
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GMAT 1: 620 Q44 V31 GMAT 2: 690 Q47 V37 GMAT 3: 610 Q47 V28 GMAT 4: 700 Q50 V34 GMAT 5: 700 Q49 V36 GMAT 6: 690 Q48 V35 GMAT 7: 750 Q49 V42 GMAT 8: 730 Q50 V39 Re: There are 42 students in a group. If each student is either  [#permalink]

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The translation of (1) killed me in this problem.
I thought it meant 4s > f. Can someone help me translate it to s > 4f?
Intern  Joined: 11 Nov 2013
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Re: There are 42 students in a group. If each student is either  [#permalink]

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