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At the beginning of the year, the Finance Committee and the Planning C
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Bunuel
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At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  25 Oct 2015, 08:15
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At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


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VikashAlex
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At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  25 Oct 2015, 09:43
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Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.


Will go with D

Given: Planning Committee (P) has 'n' members.
Finance Committee (F) has 'n' members.
Total members = n = n = 2n
Total members left (L) = 5 + 3 = 8

Find: n = ?

Statement 1:
Given that L/2n =1/6 . This implies 8/2n = k/6k (consider the ratio has multiplied by constant k). Now, 'k' value will be only 8 as it has directly given L = 8. So it will be 8/2n = 1/6. Hence, 2n = 48. ==> n=24. Hence sufficient.

Statement 2:
Given that n-3 = 21 ===> n = 24. Hence sufficient.
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  25 Oct 2015, 08:46
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Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.


(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.

=> total number of members leaving at the end of the year: 5+3 = 8
=> Total number of members in the beginning of year: 8*6 = 48
But we do not know the number of members of Planning => do not know the number of Finance

Insufficient
(2) At the end of the year, 21 members remained on the Planning Committee.

=> The number of members on the Planning: 21 + 3 = 24
=> We do not know the number of members so do not know the number of members in Finance
Sufficient

1+2 => Know the number of members in Finance => Sufficient

=> Ans: C
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  25 Oct 2015, 09:59
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At the beginning of year
Number of people in Finance committee = n
Number of people in Planning committee = n

At the end of year
Number of people in Finance committee= n-5
Number of people in Planning committee = n-3

1.
(5+3)/2n = 1/6
=>n = 48

Sufficient

2.
Number of people in Planning committee = n-3 = 21
=>n = 24

At the beginning of year ,number of people in Finance committee = 24
Sufficient

Answer D
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  26 Oct 2015, 02:22
For me also, it is D.

St 1: 8/2n = 1/6, so we can find the value of n.

St2: n-5+n-3=21 , Sufficient.

Hence the answer is D.
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  26 Oct 2015, 04:34
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1) 8/2n = 1/6, so n = 24 sufficient

2) n-3=21 so n = 24 sufficient

Hence D is the correct answer
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  21 May 2016, 14:37
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Skywalker18 wrote:
At the beginning of year
Number of people in Finance committee = n
Number of people in Planning committee = n

At the end of year
Number of people in Finance committee= n-5
Number of people in Planning committee = n-3

1.
(5+3)/2n = 1/6
=>n = 48

Sufficient

2.
Number of people in Planning committee = n-3 = 21
=>n = 24

At the beginning of year ,number of people in Finance committee = 24
Sufficient

Answer D

Hi Skywalker18! in statement 1 n=24 not 48. Please correct a typo))
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At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  07 Jun 2017, 21:36
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Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.


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.

Condition (1)
\(5 + 3 : 2n = 1: 6\)
\(2n = 48\)
Since we have 1 equation of \(n\), this is sufficient.

Condition (2)
\(n - 3 = 21\)
Since we have 1 equation of \(n\), this is also sufficient.

Therefore, D is the answer.

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: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  19 Sep 2017, 08:56
F has n employees,5 left . P has n employees 3 left
1. employees left/ total employees = 1/6
8/2n=1/6 so, n=24

2 n-3=21 so n = 24
D
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Re: At the beginning of the year, the Finance Committee and the [#permalink] New post  08 Jan 2019, 04:04
monir6000 wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Both committees have same number of members:
F=P=n
n=?

1) 8/2n = 1/6
n=24
Sufficient

2) 21+3 = 24 = n
Sufficient

Ans: D
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At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  14 Jun 2020, 08:54
Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.



"each had n members"... Does this imply that the number of members in each of the two committees is equal?
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At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  10 Jul 2020, 16:13
For me it is A.

St 1: 8/2n = 1/6, so we can find the value of n.

St2: it is not said that no members joined Planning Committee in the year, so I suppose there're m members joined Planning Committee this year.
n-3=21-m , NOT sufficient.

Hence, the answer is A.

Am I wrong? Why?
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  16 Jul 2020, 08:09
Initially:
Finance Committee = n
Planning Committee = n
Total = 2n

Year End:
Finance Committee = n - 5
Planning Committee = n - 3
Total = 2n - 8


St. 1:
8/2n = 1/6
=> n = 24

=> St. 1 is sufficient

St. 2:
n - 3 = 21
=> n = 24

=> St. 2 is sufficient

Answer: D
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At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  30 Sep 2020, 01:21
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Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.



EACH HAS N MEMBERS
SO The F+P = N+N = 2N,

(1) \(\frac{8}{2N}=\frac{1}{6}\)
2N = 48
N = 24
The member of finance committee 24.

(2) N-3= 21
N = 24
ANS. D
=
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  12 May 2021, 08:18
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Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.

Solution:

Question Stem Analysis:

We need to determine the number of members the Finance Committee had at the beginning of the year. That is, we need to determine the value of n.

Statement One Alone:

Since a total of 5 + 3 = 8 people left at the end of the year and the total number of members at the beginning of the year is n + n = 2n, we can create the proportion:

8 / (2n) = 1/6

2n = 48

n = 24

Statement one alone is sufficient.


Statement Two Alone:

Since 3 members left the Planning Committee at the end of the year and 21 members remained, the Planning Committee must have had 21 + 3 = 24 members at the beginning of the year. Since the Planning Committee and the Finance Committee had the same number of members at the beginning of the year, the Finance Committee must also have had 24 members at the beginning of the year. Statement two alone is sufficient.

Answer: D
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  22 May 2021, 23:48
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Bunuel wrote:
At the beginning of the year, the Finance Committee and the Planning Committee of a certain company each had n members, and no one was a member of both committees. At the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee. How many members did the Finance Committee have at the beginning of the year?

(1) The ratio of the total number of members who left at the end of the year to the total number of members at the beginning of the year was 1:6.
(2) At the end of the year, 21 members remained on the Planning Committee.


Kudos for a correct solution.


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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink] New post  08 Jun 2021, 07:48
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