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

Question

https://gmatclub.com/forum/download/file.php?id=47583 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 2019-04-26_1312.png

Chethan92 · Accepted Answer

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

C is the answer.

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=Myw9ERMbCmM

ZoltanBP · Answer

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

ScottTargetTestPrep · Answer

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

EMPOWERgmatRichC · Answer

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

BrentGMATPrepNow · Answer

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

IloveMBA123 · Answer

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

EMPOWERgmatRichC · Answer

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

IloveMBA123 · Answer

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?

IloveMBA123 · Answer

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?

EMPOWERgmatRichC · Answer

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

AnirudhaS · Answer

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

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

(1)+(2) x=4
Sufficient

Answer:  C

MHIKER · Answer

(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.

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=7Wc1RD0p6_Y

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards