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

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.

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

AbeNeedsAnswers wrote:

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

Given: The 9 squares above are to be filled with x's and o's, with only one symbol in each square.

Target question: How many of the squares will contain an x ?

Statement 1: More than 1/2 of the number of squares will contain an o.
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1. Here are two:
Case a: There are 5 o's and 4 x's. In this case, the answer to the target question is 4 squares contain an x
Case b: There are 6 o's and 3 x's. In this case, the answer to the target question is 3 squares contain an x
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of the 4 corner squares will contain an x.
There are several scenarios that satisfy statement 1. Here are two:
Case a: There are 5 o's and 4 x's. In this case, the answer to the target question is 4 squares contain an x
Case b: There are 4 o's and 5 x's. In this case, the answer to the target question is 5 squares contain an x
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the number of squares with an o = 5, 6, 7, 8 or 9, which means there are less than 5 squares with an x
Statement 2 tells us that there are at least 4 squares with an x
In other words: 4 ≤ (number of squares with an x) < 5
There is only one possible solution to the above inequality: x = 4
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent