swerve wrote: ↑

Fri Dec 31, 2021 5:17 am

2019-04-26_1312.png

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

The OA is C

Source: Official Guide

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