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

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Sat May 04, 2019 12:26 pm

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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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Source: Beat The GMAT — Data Sufficiency | Sat May 04, 2019 12:26 pm

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by Ian Stewart » Sat May 04, 2019 4:17 pm

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon May 13, 2019 11:49 am

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

Contact Rich at [email protected]

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SampathKp: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Nov 13, 2019 9:42 pm

by SampathKp » Wed Dec 18, 2019 5:13 am

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

From (1), more than half square contain an o means 5 or more squares contain an o. which means 0 to 4 squares can contain an X. This statement is NOT Sufficient.

From (2) If each corner square contains an X. Which means we have minimum of 4 out of 9 squares contining x. so 4 to 9 squares contain an x. this statement alone is NOT sfficient to answer the question.

Combining (1) and (2) We know that 5 squares contain an o and 4 corner squares contain an x . No other combination is possible. So both statements together are sufficient to answer the question.

Answer is C

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 18, 2019 7:16 am

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 â‰¤ (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

Brent Hanneson - Creator of GMATPrepNow.com

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