Data Sufficiency

Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second largest number of copies on Friday, did Store S sell more than 11 copies on Friday?

(1) Last week Store S sold 8 copies of the book on Thursday.
(2) Last week Store S sold 38 copies of the book on Saturday.

I got the right answer but it took me a while. Can any one suggest a short and qucik way to solve such kind of problems. Any help is appreciated.

Best Regards,
JOHN

m+t+w+th+f+s+su=90
s >f>every other day. f>11??
a) th=8. remaining 6 = 82. we can take f=10 and arrange others such that total becomes 90 and all conditions are satisfied and same thing can be done by taking f=12. Thus insufficient
b) s=38. thus remaining 6 = 52.
in remaining 6, f is max and <38 (as f<s)
if m,t,w,th,su=1+2+3+4+5, f >11.
if f=11,m+t+w+th+su can be max (10+9+8+7+6) = 40. thus if f=11,we can't get 52 total.
thus f>11. Sufficient
IMO B

We are told in statement 2 that the number of books sold on Saturday was 38, from the prompt it says that, on Saturday the maximum books were sold, and on Friday the second largest number of books were sold. This leaves no doubt then that on Friday the number of books that had to be sold was 37 and the remaining 15 books would have be sold on the other 5 days.

In statement 1, we could have different cases where on Friday the store could have sold less than 11 or more than 11 by varying the number of books sold on Saturday

here the concept is sum and value - we are told they add up to 90, Sat is greatest, Fri is second greatest - there are 5 other days that are less than Friday.

statement 1 - if Thur = 8 then that just says that Fri and Sat could be higher than 8 - if F = 11 then we cold have any number for Saturday so saturday can make up any difference betweeen the lower sums and 90 - thus it is insufficient.

Statement 2 - if Sat = 38 then we have to figure out how much is left in the sum: 90 - 38 = 52 so all the other numbers have to add up to 52 - the question asks if F= 11 therefore let's see what happens when f = 11 (we would have 41 left for the last five numbers). Now we have to remember that Friday is the second highest number which means that all other five days must be below 10 and they must be different - therefore the largest sum we can have is 10+9+8+7+6 = 40 but we needed them to add up to 40 - so it is impossible for f = 11. Therefore it is sufficient and the answer is B.

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