I think the answer is E also, but for different reasons. I might be over thinking the problem. Would appreciate feedback.
Statement 1: From this statement, I can gather that they have enough data from enough days to say the following...
First, there's been enough less-than-5-book-days to give a percentage of customers who ultimately buy the book after viewing of 46%.
Second, similarly, there's been enough more-than-5-book days to give a percentage of 47%.
Third, the company has rounded, so we can say more accurately...
x = books bought during less-than-5-book-days
c = customers views
45.5% <= x/c < 46.5%
.455c <= x and x < .465c
y = books bought during more-than-(or equal to)-5-book-days
d = customer views
46.5% <= y/d < 47.5%
.465d <= y < .475d
In addition, x, y, c, d are all whole numbers.
The smallest that x can be is 6 (with c = 13), and the smallest that y can be is 7 (with d = 15).
So, we know the company sold at least 13 books based on statement 1, but they could have sold a lot more as well. We can hope that they are basing their data off more than 13 books sales, but we can't know. Statement 1 is insufficient by itself.
Statement 2: From this statement, I gather the following...
c = initial customers
b = books sales
b/c = 47%
b/(c+10) = 46%
But since, the company rounded, we can more accurately say...
46.5% <= b/c < 47.5%
45.5% <= b(c+10) < 46.5%
Solving for b...
.465c <= b and b < .475c
.455c + 4.55 <= b and b < .465c + 4.65
And since, b and c must be whole numbers...
...(using a spreadsheet to check values of c, starting at 1)...
...the smallest possible value of b is 112 (with c = 236 and c + 10 = 246).
So, we know that they sold at least 112 books on one particular day, but we don't know anything else about any other days, so this is insufficient by itself.
Statement 1 and 2:
Assuming that the company sold 112 books in one day with 46% conversion rate, how many books did they have to sale on other days, to make their more-than-(or equal to)-five-book-day average 47%?
Let y = books bought during more-than-5-book days (excluding the 112-book-sale day)
Let d = customer views (excluding the 246 views on the 112-book-sale day)
46.5% <= (y + 112)/(d + 246) < 47.5%
.465(d +246) - 112 <= y and y < .475(d + 246) - 112
And d >= y (since the company can't sell more than 1 book to a single customer)
A single day of 5 customer views and 5 book sales satisfy the above equations and raise the conversion rate to 46.6%.
So, we can conclude that at the very least the company sold...
6 books--we know they sold at least 6 books during their less-than-5-book-days based on statement 1.
112 books--we know they sold at least 112 books on one day based on Statement 2.
5 books--We know they had at least one more 5-book-day based on Statement 1 and 2 combined.
6 + 112 + 5 = 123
So, Statement 1 and 2 are insufficient.
