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

Let \(n\) be the number of squares that will contain an \(x\). The original question: \(n=?\)

1) We know that the number of o's will be at least 5, so \(n\) can be any integer in the interval \(0\leq n\leq 4\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

2) We know the the number of x's will be at least 4, so \(n\) can be any integer in the interval \(4\leq n\leq 9\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

1&2) There's only one valid case based on all information, x's in the corner squares and o's in all other 5 squares, so \(n=4\). Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

Answer: C

Statement One Alone:

More than 1/2 of the number of squares will contain an o.

That is, at least 5 of the 9 squares will contain an o. In other words, at most 4 squares will contain an x. However, we still can’t determine the exact number of squares that will contain an x.

Statement one alone is not sufficient.

Statement Two Alone:

Each of the 4 corner squares will contain an x.

We see that at least 4 of the 9 squares will contain an x. However, we still can’t determine the exact number of squares that will contain an x.

Statement two alone is not sufficient.

Statement One and Two Together:

Statement one tells us that at most 4 squares will contain an x, and statement two tells us that at least 4 squares will contain an x. Therefore, exactly 4 squares will contain an x.

The two statements together are sufficient to answer the question.

Answer: 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:

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

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

Hi All,

Need help on the English "Each of the 4 corner squares will contain an X" What does this mean?

According to dictionary "corner" means a place or angle where two sides or edges meet. I can only see 4 corners

Hi waihoe520,

Your understanding is correct; there are only 4 'corners' in this shape - so the 4 "corner squares" are the 4 squares that touch those corners. Based on the information in Fact 2, the 4 corner squares would each have an "X" in them, so you know that AT LEAST 4 X's will appear in the grid.

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

Thank you sir! How would you reword the statement 2 to be "only 4 Xs" instead of "at least 4Xs"

There are 4 Xs on each of the corners?

Thank you sir! How would you reword the statement 2 to be "only 4 Xs" instead of "at least 4Xs"

There are 4 Xs in each of the corners?

Hi waihoe520,

The opening prompt tells us that EACH of the 9 squares in the grid contains ONE symbol (an "X" or an "O"), so we know that there will be 9 symbols in TOTAL.

Fact 2 tells us that the 4 corners each contain an "X" - so that means that there are going to be AT LEAST 4 "Xs" among the 9 squares (but from that information, we don't know what symbols are in the other 5 squares - there might be some additional Xs or there might not be any).

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

(1) x = 4,3,2,1
Insufficient

(2) x = 4,5,6,7,8,9
Insufficient

(1)+(2) x=4
Sufficient

Answer: C

(1) 5 can be 0, or all 9 can be 0 and no x insufficient.

(2) All squares with the corners' 4 can be x. Insufficient

Considering both:

If the corners' are x and more than half are 0 then there will be 4 x and 5 0. Sufficient.

Answer: Option C

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