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

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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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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]
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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]
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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]
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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.

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At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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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.

Video solution by GMATinsight

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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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.

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.

Please let me know where am I wrong and how can i not do this mistake from next time ?
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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piyushluniya wrote:
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.

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.

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.
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At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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.

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.
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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Kimberly77 wrote:
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.

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.
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]
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.
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Re: At the beginning of the year, the Finance Committee and the Planning C [#permalink]