At the beginning of the year, the Finance Committee and the Planning C

(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

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

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

Hence D is the correct answer

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
=

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

Answer: Option D

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Hi Bunuel VeritasKarishma
For 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.

Please let me know where am I wrong and how can i not do this mistake from next time ?

Statement 2 tells us that 21 members "remained". It means they did not leave. Hence the 21 does not include anyone who joined. They were those who were present at the beginning of the year too.

Hi BrentGMATPrepNow, Given

At the beginning of year
Number of people in Finance committee = n
Number of people in Planning committee = n
Total = 2n

At the end of year
Number of people in Finance committee= n-5
Number of people in Planning committee = n-3
Total = 2n - 8

For St1, wondering why is not 2n-8/2n = 1/6 but 8/2n? Not sure what did I miss? Thanks Brent.

Statement 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.
We're told that, at the end of the year, 5 members left the Finance Committee and 3 members left the Planning Committee.
So, the total number of members who left = 5 + 3 = 8.

Your equation is for a different statement.
REVISED statement 1: The ratio of the total number of members who remained after 8 members left at the end of the year to the total number of members at the beginning of the year was 1:6.
IF this were the wording for statement 1, your equation, (2n-8)/2n = 1/6 would apply.

Clear statement 1 is sufficient. But for 2, couldn´t it be the case that people left throughout the year, and not only at the end of the year? Example: suppose 2 year left throughout the year, then n=21+3(left at the end of the year)+2 (left at other points of the year) =26.

­The phrase "At the end of the year, 3 members left the Planning Committee," implies that the 3 members left the committee during the course of the year, not necessarily exactly at the end. This phrasing typically indicates a timeframe spanning the entire year, and is not restricted to the very last moment of the year. Therefore, the situation you're describing, where additional members leave at different times, does not apply.