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 xCase b: There are 6 o's and 3 x's. In this case, the answer to the target question is
3 squares contain an xSince 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 xCase b: There are 4 o's and 5 x's. In this case, the answer to the target question is
5 squares contain an xSince 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 xStatement 2 tells us that
there are at least 4 squares with an xIn other words: 4 ≤ (number of squares with an x) < 5
There is only one possible solution to the above inequality:
x = 4Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent