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Master | Next Rank: 500 Posts
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by Abdulla » Tue Nov 24, 2009 8:12 pm
Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

1) Last week Store S sold 8 copies on Thursday
2) Last week Store S sold 38 copies on Saturday

OA is B
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Source: — Data Sufficiency |
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by sunnyjohn » Wed Nov 25, 2009 12:28 am
Cool question...
Time consuming as well..
Well lets look at the solution..!

overall we have to distribute 90 books into 7 different parts.
and by doing that - can we tall that second highest part is greater than 11?

Option A)
one part is 8. Hmm, Now Friday part( Second highest) can be 9 or 12. So INSUFFICIENT

Option B)
highest part 38.
so now we have 90 - 38 = 52 books to be divide into 6 DIFFERENT parts.

lets take 2 cases:

Friday = 10 Books := 52-10 = 42 books to 5 parts with each part less than 10. Even 9,8,7,6,5 do not sum to 42.
so Friday book has be greater than 10.

Friday = 11 Books : = 52 - 11 = 41 books to 5 parts with each part less than 11. Even 10,9,8,7,6 do not sum to 41.
so Friday book has be greater than 11.

Its proved that friday books has be greater than 11.
Still for proof;
Friday = 12 books : 52 - 12 = 40 books --> 5 days :- 10,9,8,7,6 ==> 40 books...!
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by Abdulla » Wed Nov 25, 2009 1:03 am
sunnyjohn wrote:Cool question...
Time consuming as well..
Well lets look at the solution..!

overall we have to distribute 90 books into 7 different parts.
and by doing that - can we tall that second highest part is greater than 11?

Option A)
one part is 8. Hmm, Now Friday part( Second highest) can be 9 or 12. So INSUFFICIENT

Option B)
highest part 38.
so now we have 90 - 38 = 52 books to be divide into 6 DIFFERENT parts.

lets take 2 cases:

Friday = 10 Books := 52-10 = 42 books to 5 parts with each part less than 10. Even 9,8,7,6,5 do not sum to 42.
so Friday book has be greater than 10.

Friday = 11 Books : = 52 - 11 = 41 books to 5 parts with each part less than 11. Even 10,9,8,7,6 do not sum to 41.
so Friday book has be greater than 11.

Its proved that friday books has be greater than 11.
Still for proof;
Friday = 12 books : 52 - 12 = 40 books --> 5 days :- 10,9,8,7,6 ==> 40 books...!
Good job, but can't you get a shortcut or quick steps to get the answer?
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by sadullaevd » Thu Nov 26, 2009 2:43 am
sunnyjohn wrote:Cool question...
Time consuming as well..
Well lets look at the solution..!

overall we have to distribute 90 books into 7 different parts.
and by doing that - can we tall that second highest part is greater than 11?

Option A)
one part is 8. Hmm, Now Friday part( Second highest) can be 9 or 12. So INSUFFICIENT

Option B)
highest part 38.
so now we have 90 - 38 = 52 books to be divide into 6 DIFFERENT parts.

lets take 2 cases:

Friday = 10 Books := 52-10 = 42 books to 5 parts with each part less than 10. Even 9,8,7,6,5 do not sum to 42.
so Friday book has be greater than 10.

Friday = 11 Books : = 52 - 11 = 41 books to 5 parts with each part less than 11. Even 10,9,8,7,6 do not sum to 41.
so Friday book has be greater than 11.

Its proved that friday books has be greater than 11.
Still for proof;
Friday = 12 books : 52 - 12 = 40 books --> 5 days :- 10,9,8,7,6 ==> 40 books...!

Great job, well explained.

I guess we could have shortcut by plugging 11 straightaway, since its obvious that if numbers don't sum up when you plug 11, then the number should be greater than 11. You don't need to check 2 cases(time consuming) as time is limited on GMAT.

cheers
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