Max@Math Revolution wrote:Is x/y > 1?
1) x > y
2) x - y > 1
Target question: Is x/y > 1?
Statement 1: x > y
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is
YES, x/y IS greater than 1
Case b: x = 3 and y = -1. In this case, x/y = 3/(-1) = -3. So, the answer to the target question is
NO, x/y is NOT greater than 1
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x - y > 1
Let's TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is
YES, x/y IS greater than 1
Case b: x = 3 and y = -1. In this case, x/y = 3/(-1) = -3. So, the answer to the target question is
NO, x/y is NOT greater than 1
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the
same counter-examples to show that each statement ALONE is not sufficient.
So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is
YES, x/y IS greater than 1
Case b: x = 3 and y = -1. In this case, x/y = 3/(-1) = -3. So, the answer to the target question is
NO, x/y is NOT greater than 1
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
