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matrix table method

by buoyant » Thu Dec 25, 2014 6:09 pm
35 percent of the books in Richard's collection are novels and
60 percent of the books are paperbacks. If 20 percent of the
paperbacks in Richard's collection are novels published
before 1940, how many of the paperbacks in Richard's
collection are novels published before 1940.
(1) Non-Â…fiction books make up exactly half of Richard's
collection.
(2) 100 of the books in Richard's collection are non-fiction

[spoiler]OA:C[/spoiler]

what are the entities in the matrix table columns and rows?
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Source: — Data Sufficiency |

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by [email protected] » Thu Dec 25, 2014 8:42 pm
Hi buoyant,

This is a far more complex Overlapping Sets question than you would typically see on Test Day. Instead of the typical "2 groups and their opposites" that you'll have in a Tic-Tac-Toe board question, you actually have 4 groups:

Novels and Not-Novels
Paperbacks and Not-paperbacks
Before 1940 and During/After 1940
Non-Fiction and Fiction

Even with this degree of complexity, you could still use the Tic-Tac-Toe board, BUT you would have to keep track of information OUTSIDE of the board.

The interesting thing is that you can solve it WITHOUT the Tic-Tac-Toe board though. You just have to stay organized with your notes...

From the prompt, we can break down Richard's collection into the following...

35% are novels, so 65% are NOT novels
60% are paperbacks, so 40% are NOT paperbacks

20% of the PAPERBACKS (so 20% of the 60%) are NOVELS published BEFORE 1940
20% of 60% = (.2)(.6) = .12 = 12%

So 12% of the TOTAL books are PAPERBACKS that are NOVELS published BEFORE 1940.

We're asked HOW MANY BOOKS make up that 12%.

Fact 1: NON-FICTION books make up exactly HALF of the collection.

This information does not connect, in any way, to the information that we already have. There's no way to derive a value from it or figure out a value for any category of book.
Fact 1 is INSUFFICIENT

Fact 2: 100 books are NON-FICTION

This information also does not connect, in any way, to the information that we already have.
Fact 2 is INSUFFICIENT

Combined though, we do learn something..
HALF the books are NON-FICTION
100 books are NON-FICTION

Thus, the TOTAL number of books is 200.
The question asked us for the TOTAL number of books that are PAPERBACKS and that are NOVELS published BEFORE 1940. We KNOW that 12% of the books fit that description, so 12% of 200 is the answer (24 books).
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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