AAPL wrote:A shelf contains hardcover and paperback books, of either fiction or nonfiction. How many books are on the shelf?
1) 2/3 of the books are fiction and 1/4 of the books are hardcover.
2) Fewer than 30 books are paperback and more than 10 are nonfiction.
This is an EITHER/OR group question.
Every book is EITHER hardcover OR paperback.
Every book is EITHER fiction OR nonfiction.
For an EITHER/OR group problem, use a DOUBLE-MATRIX to organize the data.
There are two fractions in statement 1: 2/3 and 1/4.
Since the product of the denominators = 4*3 = 12, let the TOTAL = 12x.
Here's the matrix:
_______________F______NF_______Total
H:
P:
Total:___________________________12x
Values in the matrix must add up horizontally and vertically.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.
Statement 1; 2/3 of the books are fiction and 1/4 of the books are hardcover.
Thus, total fiction = (2/3)12x = 8x, and total hardcover = (1/4)12x = 3x.
The result is the following:
________________F______NF______Total
H:_______________________________3x
P:________________________________9x
Total:_________8x______4x______12x
No way to determine the value of 12x.
INSUFFICIENT.
Statement 2: Fewer than 30 books are paperback and more than 10 are nonfiction.
No way to determine the total number of books.
INSUFFICIENT.
Statements combined:
The matrix indicates that total P = 9x and total NF = 4x.
Thus:
9x < 30, implying that x < 10/3.
4x > 10, implying that x > 5/2.
Thus, x = 3, implying that the total number of books = 12x = 12*3 = 36.
SUFFICIENT.
The correct answer is
C.
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