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by sunilrawat » Sat Aug 27, 2011 2:16 am
At Consolidated Foundries, for a resolution to become policy, a quorum of at-least half the 20 directors must pass the resolution by at-least a two-thirds majority. At a meeting of the board of directors, did resolution X pass or fail?
1. 10 directors voted for the resolution
2. 7 directors voted against the resolution.

OA B
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Aug 27, 2011 3:36 am
sunilrawat wrote:At Consolidated Foundries, for a resolution to become policy, a quorum of at-least half the 20 directors must pass the resolution by at-least a two-thirds majority. At a meeting of the board of directors, did resolution X pass or fail?
1. 10 directors voted for the resolution
2. 7 directors voted against the resolution.

OA B
Let F = votes for the resolution, A = votes against, T = total votes.

Question rephrased: Is F > (2/3)T? or Is A < (1/3)T?

Statement 1: F = 10.
10 > (2/3)T?
T < 15?
Since it's possible that T < 15 or that T ≥ 15, insufficient.
If there are 11 total votes -- 10 for, 1 against -- the resolution passes.
If there are 20 total votes -- 10 for, 10 against -- the resolution does not pass.

Statement 2: A = 7.
7 < (1/3)T?
T > 21?
In order for the resolution to pass, there must be at least 21 votes.
Since the greatest number of votes could be 20, the resolution does not pass.
Sufficient.

The correct answer is B.
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by Brent@GMATPrepNow » Sun Dec 23, 2018 11:03 am
sunilrawat wrote:At Consolidated Foundries, for a resolution to become policy, a quorum of at-least half the 20 directors must pass the resolution by at-least a two-thirds majority. At a meeting of the board of directors, did resolution X pass or fail?
1. 10 directors voted for the resolution
2. 7 directors voted against the resolution.

OA B
Given: A quorum of at least half the 20 directors must pass the resolution by at least a two-thirds majority

Target question: At a meeting of the board of directors, did resolution X pass or fail? 

Statement 1: Ten directors voted for the resolution. 
KEY: We don't know how many directors attended the meeting.
Let's test some possible scenarios that satisfy statement 1:
Case a: 12 directors attended, and 10 of them voted FOR the resolution. Since 10/12 > 2/3, the answer to the target question is YES, the resolution passed
Case b: 20 directors attended, and 10 of them voted FOR the resolution. Since 10/20 < 2/3, the answer to the target question is NO, the resolution did NOT pass
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Seven directors voted against the resolution
Let's examine all possible cases:
Case a: 7 directors attended the meeting. Since we need at least 10 directors to form a quorum, the resolution did NOT pass
Case b: 8 directors attended the meeting. Since we need at least 10 directors to form a quorum, the resolution did NOT pass
Case c: 9 directors attended the meeting. Since we need at least 10 directors to form a quorum, the resolution did NOT pass
Case d: 10 directors attended, and 7 voted AGAINST. So 3 voted FOR the resolution. Since 3/10 < 2/3, the resolution did NOT pass
Case e: 11 directors attended, and 7 voted AGAINST. So 4 voted FOR the resolution. Since 4/11 < 2/3, the resolution did NOT pass
Case f: 12 directors attended, and 7 voted AGAINST. So 5 voted FOR the resolution. Since 5/12 < 2/3, the resolution did NOT pass
.
.
.
.
Case n: 20 directors attended, and 7 voted AGAINST. So 13 voted FOR the resolution. Since 13/20 < 2/3, the resolution did NOT pass

Since the answer to the target question is the SAME every time, statement 2 is SUFFICIENT

Answer: B

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