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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(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

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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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.

1) 8/2n = 1/6, so n = 24 sufficient

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

Hence D is the correct answer

Hi Skywalker18! in statement 1 n=24 not 48. Please correct a typo))
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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.

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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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

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

"each had n members"... Does this imply that the number of members in each of the two committees is equal?

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?

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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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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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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Answer: Option D

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