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805+ (Hard)|   Math Related|      
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Sajjad1994
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Ross and Ralph are running for school president at a university with a Updated on: 06 Oct 2023, 07:45
Originally posted by Sajjad1994 on 29 Mar 2021, 06:30.
Last edited by BottomJee on 06 Oct 2023, 07:45, edited 5 times in total.
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Ross
Wins: Ross wins the college of Arts & Letters. Ralph
Wins: Ross wins three colleges but Ralph earns more electoral votes.
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95% (hard)

Question Stats:

41% (03:12) correct 59% (03:21) wrong based on 266 sessions

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Ross and Ralph are running for school president at a university with an electoral college system. The candidate who wins the most votes within any one college wins all of the electoral votes for that college, and the candidate who wins a majority (greater than half) of the electoral college votes wins. There are 428 electoral votes total, but the campus is split between some colleges that vote on Tuesdays and some that vote on Wednesdays.

After Tuesdays votes are tabulated, Ross has 182 votes and Ralph has 177, with the following colleges left to vote:

CollegeNumber of
Electoral Votes
Architecture8
Arts & Letters38
Engineering10
Music5
Veterinary Studies8

From the answer choices below, please select one situation for Wednesday's election that guarantees Ross wins the presidency and one that guarantees Ralph wins the presidency. Make only one selection in each column.
Ross
Wins 		Ralph
Wins
Ross wins four colleges and Ralph wins one.
Ralph wins four colleges and Ross wins one.
Ross wins the college of Arts & Letters.
Ross wins three colleges and Ralph wins two
Ross does not win any electoral votes.
Ross wins three colleges but Ralph earns more electoral votes.
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Ross
Wins: Ross wins the college of Arts & Letters. Ralph
Wins: Ross wins three colleges but Ralph earns more electoral votes.
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Ross and Ralph are running for school president at a university with a 27 Feb 2022, 16:49
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If Ross did not win any electoral votes, Ralph would have these votes. Why is the fifth option incorrect "for Ralph wins"?
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Ross and Ralph are running for school president at a university with a 28 Feb 2022, 03:17
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AndreMarchan
If Ross did not win any electoral votes, Ralph would have these votes. Why is the fifth option incorrect "for Ralph wins"?
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It is not mentioned in the question that if one candidate has not won then the same voters will go to its opponents. Hence the highlighted text above can be correct.
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Ross and Ralph are running for school president at a university with a 28 Feb 2022, 04:43
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Ross wins four colleges and Ralph wins one. - Cannot be considered as the correct answer, because it is not mentioned which college does Ross win and which one Ralph wins. There are 'n' number of possibilities to look at.

Ralph wins four colleges and Ross wins one. - Cannot be considered as the correct answer, because it is not mentioned which college does Ralph win and which one Ross wins. There are 'n' number of possibilities to look at.

Ross wins the college of Arts & Letters. - This is the correct answer as winning this college clearly secures the election for Ross. Even if Ralph wins all the other colleges in no scenario will he be able to get more votes than Ross.

Ross wins three colleges and Ralph wins two - Same reasoning as the first two.

Ross does not win any electoral votes. - Ross may not win any electoral vote but we do not know whether Ralf won all ,or was their a tie between the two ?

Ross wins three colleges but Ralph earns more electoral votes - This is the correct answer as the only possible scenario where Ralph wins more electoral votes than Ross is when Ross wins the Arts & Letters college and any of the other college, which puts his total votes higher than Ross's despite Ross winning 3 colleges.
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Ross and Ralph are running for school president at a university with a 15 Mar 2022, 10:32
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Official Explanation

With 428 electoral votes total, the winner needs to have 215 votes to have a majority. So Ross needs 33 votes and Ralph needs 38 votes, with 69 votes left to be cast. The college of Arts & Letters is the big prize with 38 votes, leaving only 31 votes split between the remaining colleges. So in order to win, either candidate would need to win Arts & Letters. Ross’ path to that win is clearly laid out in the answer choices with choice C. But Ralph’s is obscured in choice F – any sum of three colleges adds up to more than the 10 votes available with the second-biggest college, meaning that for F to be true Ralph would have to win the College of Arts & Letters and therefore the presidency. Beware of choice E – just because Ross does not win any electoral votes does not mean that Ralph automatically wins them all. The stimulus does not guard against a third candidate.  

Answer:

Ross Wins: Ross wins the college of Arts & Letters.
Ralph Wins: Ross wins three colleges but Ralph earns more electoral votes
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Ross and Ralph are running for school president at a university with a 24 Feb 2024, 02:32
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Sajjad1994 what if Ross wins Arts College with 20 votes, The balance 49 votes go to Ralph. In that case, with C True, Ross doesn't get the guarantee to win the election right?
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Ross and Ralph are running for school president at a university with a 24 Feb 2024, 05:26
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Shrey~
Sajjad1994 what if Ross wins Arts College with 20 votes, The balance 49 votes go to Ralph. In that case, with C True, Ross doesn't get the guarantee to win the election right?
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­You are right! But we have to go with the choices available.
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Ross and Ralph are running for school president at a university with a 14 Sep 2024, 08:02
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Shrey1
Sajjad1994 what if Ross wins Arts College with 20 votes, The balance 49 votes go to Ralph. In that case, with C True, Ross doesn't get the guarantee to win the election right?
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But if Ross wins Arts College with 20 out of 38 votes he automatically wins all the 38 votes of Arts College and that guarantees his win.
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