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

[BTGmoderatorDC]

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.

OA D

Source: Official Guide

[Jay@ManhattanReview]

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.

OA D

Source: Official Guide

We know that the number of members in the finance committee and in planning committee are n, each.

At the end of the year, the number of members in the finance committee and in planning committee would be (n - 5) and( n - 3), respectively.

We have to determine how many members did the Finance Committee have at the beginning of the year?

Question: What's the value of n?

Let's take each statement one by one.

(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.

=> 2n/8 = 1/6 => n = 24. Sufficient.

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

=> n - 3 = 21 => n = 24. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

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.

OA D

Source: Official Guide

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