Six Countries

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Kumar007: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Feb 10, 2009 5:07 pm; Thanked: 1 times

by Kumar007 » Wed Apr 01, 2009 2:38 am

Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if country A sent the second highest number of representative, did country A send at least 10 representatives?

1. One of the six countries sent 41 representatives to the congress.
2. Country A sent fewer than 12 representatives to the congress.

Answer E
Can someone please explain the solution for this problem.

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 01, 2009 2:38 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Wed Apr 01, 2009 3:03 am

1) A cant send 41, for if A sent 41, A being second highest, the highest would have been greater than 41 and we would have > 75

so the highest is 41. we have 75-41=34 reps to be distributed between A and the other 4 countries. a way to do this would be arrange them in descending order as no countries have the same number of reps.

say A =10, we can have the arrangements as 41+ 10+9+8+5+2=75
say A= 9, we can have the arrangements as 41+9+8+7+6+4=75

not sufficient as A can be greater or less than 10.

2) A<12
say A=11, we can have 30+11+10+9+8+7=75
say A=9, we can have 40+9+8+7+6+5=75

not sufficient as A can be greater or less than 10

taking both statements together we can have the same examples used for statement 1.
not sufficient

hence E

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Tue Jul 10, 2012 9:17 pm

dravv a number line

1 ----------2------------3--------------4-------------5----------6

6Min 7 .............. 41 =75

So A< 10

41 10 ............................ 6

A= 10

similarly another line you can get vvhere A 11

So E
Since you cannot prove either vvays on vvhat A is

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benjiboo: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Sep 24, 2009 2:38 pmFollowed by: 9 members; Location: NYC; Thanked: 33 times; GMAT Score:710

by benjiboo » Sun Sep 23, 2012 4:24 pm

Please explain "6min 7.....41=75" and what it means, specifically, the "6min7"

venmic wrote:dravv a number line

1 ----------2------------3--------------4-------------5----------6

6Min 7 .............. 41 =75

So A< 10

41 10 ............................ 6

A= 10

similarly another line you can get vvhere A 11

So E
Since you cannot prove either vvays on vvhat A is

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