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Six countries in a certain region sent a total of 75

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Six countries in a certain region sent a total of 75 [#permalink]

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New post 27 Jul 2009, 00:54
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Difficulty:

  55% (hard)

Question Stats:

68% (01:38) correct 32% (01:50) wrong based on 131 sessions

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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 greatest number of representatives, 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: six-countries-in-a-certain-region-sent-a-total-of-93368.html
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Re: Six countries in a certain region sent a total of 75 [#permalink]

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New post 27 Jul 2009, 01:10
uzonwagba wrote:
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 greatest number of representatives, 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.


IMO E,

1. Is not suff, lets say for. e.g A sent 9 rep then the other 4 countries would have sent 8,7,6,4 which totals to 75 or and we can also assume that country A sent 10 then also we can have various options for other 4 countries.

2. Similarly this is also not suff.

Even if we combine then also its not suff.
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Re: Six countries in a certain region sent a total of 75 [#permalink]

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New post 27 Jul 2009, 01:37
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I get E.

1) Max is 41. So A < 41.
Remaining is 75-41 = 34

If A sends 10, the max total from remaining companies can be 10+9+8+7+6 = 40. This is okay because total of max remaining should be greater than 34. ( In order to deduct 6 we can adjust the numbers for remaining companies )

If A sends 9, the max total for remaining will be 9+8+7+6+5=35. This is also okay because 35>34.

So we don't know for sure whether A has sent >=10.

2) A sends less than 12.
A can send 11,10,9,8,..5 as we don't know the greatest number of employees that a company has sent.

Combining,
A can send 11,10 or 9. So E.

Note that if A sends 8, then max total for remaining will be 8+7+6+5+4 = 30 < 34. So A > 8. However this does not answer our question.
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Re: Six countries in a certain region sent a total of 75 [#permalink]

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New post 22 Sep 2014, 00:18
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Re: Six countries in a certain region sent a total of 75 [#permalink]

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New post 02 Dec 2017, 20:27
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Re: Six countries in a certain region sent a total of 75   [#permalink] 02 Dec 2017, 20:27
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