Bunuel wrote:
Was the number of books sold at Bookstore X last week greater than the number of books sold at Bookstore Y last week?
(1) Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday
(2) Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday
We need to determine whether the number of books sold at Bookstore X last week was greater than the number of books sold at Bookstore Y.
Statement One Alone:Last week, more than 1,000 books were sold at Bookstore X on Saturday and fewer than 1,000 books were sold at Bookstore Y on Saturday.
Knowing the number of books that were sold on one day of the week is not enough information to determine whether, for the entire week, the number of books sold at Bookstore X was greater than the number of books sold at Bookstore Y. Statement one alone is not sufficient. We can eliminate answer choices A and D.
Statement Two Alone:Last week, less than 20 percent of the books sold at Bookstore X were sold on Saturday and more than 20 percent of the books sold at Bookstore Y were sold on Saturday.
Since we do not know how many books were sold on Saturday, we cannot determine how many books were sold last week at either Bookstore X or Bookstore Y.
Statements One and Two Together:Using the information from statements one and two, we can define the following variables:
x = the number of books sold at Bookstore X last week
y = the number of books sold at Bookstore Y last week
s = the number of books sold at Bookstore X on Saturday (note: s > 1,000)
t = the number of books sold at Bookstore Y on Saturday (note: t < 1,000)
p = percent of books at Bookstore X sold last week that were sold on Saturday (note: p < .2)
q = percent of books at Bookstore Y sold last week that were sold on Saturday (note: q > .2)
Using our variables, we can create the following equations:
x = s/p
and
y = t/q
We need to determine whether x > y, or s/p > t/q, or sq > pt. Since s > t and q > p, and all values are positive, we can determine that sq is greater than pt, and thus that x > y.
Answer: C
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