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The 9 squares above are to be filled with x's and o's

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The 9 squares above are to be filled with x's and o's

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The 9 squares above are to be filled with x's and o's, with only one symbol in each square. How many of the squares will contain an x ?

(1) More than 1/2 of the number of squares will contain an o.
(2) Each of the 4 corner squares will contain an x.

C

Source: Official Guide 2020

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From Statement 1, we know we have at least 5 O's, and therefore at most 4 X's.

From Statement 2, we know we have at least 4 X's, in the four corners.

Neither statement is sufficient, but using both, if we have at least 4 X's and at most 4 X's, we must have exactly 4 X's, and the two statements are sufficient together, so the answer is C.

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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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Hi All,

We're told that the 9 squares above are to be filled with X's and O's, with only one symbol in each square. We're asked for the number of squares that will contain an X. This question is based around some simple Arithmetic and logic - although you might find it useful to draw a few pictures to keep organized.

(1) MORE than 1/2 of the number of squares will contain an O.

In this prompt, you cannot have a 'fraction' of a square, so MORE than 1/2 of the 9 squares means AT LEAST 5 of the 9 squares will contain an O. This means that no more than 4 of the squares can hold an X, but that could be 0, 1, 2, 3 or 4 squares.
Fact 1 is INSUFFICIENT

(2) Each of the 4 corner squares will contain an X.

With the information in fact 2, we know that AT LEAST 4 of the squares (the 4 corner squares) will contain an X, but we don't know how many total squares will hold an X; it could be 4, 5, 6, 7, 8, or 9 squares.
Fact 2 is INSUFFICIENT

Combined, we know...
-More than 1/2 of the number of squares will contain an O.
-Each of the 4 corner squares will contain an X.

Based on the possibilities we defined in each of the two Facts, the only possible value that fits BOTH Facts is "4" (re: 4 X's in the four corners and 5 O's in the other squares).
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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