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Could you please help me with this issue (with the explanation please):
At Consolidated Foundries, for a resolution to become policy, a quorum of at least half of 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) Ten directors voted for the resolution. 2) Seven directors voted against the resolution.
Question tells us that for a resolution to pass we must have atleast = 10*2/3 = 6.67 => 7 votes, in favor of resolution.
Statement 1: Tells us 10 directors voted for the resolution. Means half of 20 directors voted, but does not tells us how many voted in favor and how many voted against it.
Statement 2: Tells us 7 directors voted against the resolution. Now here is the catch. 20*1/3 (2/3 needed for passing so 1/3 needed for failing it) = 6.67 => 7. If 7 directors vote against a resolution then resolution will fail. So this statement alone is able to answer the question.
First of all, forgot about statement 1 when answer only statement 2. So we are not given whether 7 out of 10 people voted against resolution or 7 out of 20 people voted against resolution.
If 7 out of 10 people voted against resolution then only 3 people voted in favor of resolution, which is less than needed 2/3 of 10 majority so resolution will fail.
If 7 out of 20 people voted against resolution then only 13 people voted in favor of resolution, which is again less than needed 2/3 of 20 majority (majority is 13.33, in absolute terms it will be 14) so resolution will fail.
I took case of 20 only because if resolution is failing with larger group, then with same number of against votes it will definitely fail with smaller group.