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

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Difficulty:   5% (low)

Question Stats: 79% (01:01) correct 21% (00:58) wrong based on 357 sessions

### HideShow timer Statistics 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.

DS52602.01
OG2020 NEW QUESTION

Attachment: 2019-04-26_1312.png [ 2.18 KiB | Viewed 3153 times ]

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Re: The 9 squares above are to be filled with x's and o's, with only one  [#permalink]

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1
From S1:

More than half of the squares are O's
Means > 5
O's can be 5,6 or 7.
Hence Insufficient.

From S2:

Each corner is X's.
But no info about other squares.
Insufficient.

Combining both:
Number of O's = 5 (More than half of the squares are O's)
Number of X's = 4

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Re: The 9 squares above are to be filled with x's and o's, with only one  [#permalink]

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Bunuel 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.

DS52602.01
OG2020 NEW QUESTION

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

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Re: The 9 squares above are to be filled with x's and o's, with only one  [#permalink]

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Bunuel 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.

DS52602.01
OG2020 NEW QUESTION

Attachment:
2019-04-26_1312.png

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.

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Re: The 9 squares above are to be filled with x's and o's, with only one  [#permalink]

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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

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Re: The 9 squares above are to be filled with x's and o's, with only one  [#permalink]

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Top Contributor
Bunuel 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.

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

Cheers,
Brent
_________________ Re: The 9 squares above are to be filled with x's and o's, with only one   [#permalink] 18 Dec 2019, 08:34
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