macwanjason wrote:
If [x] denotes the least integer greater than or equal to x, is [x] = 0?
(1) -1< x< 1
(2) x < 0
Target question: Is [x] = 0?This is a good candidate for
rephrasing the target question.
Given: [x] denotes the least integer greater than or equal to x Let's make sure we understand what this [] symbol means.
Here are a few examples:
[3.1] = 4
[5.8] = 6
[0.7] = 1
[-0.9] = 0
[0] = 0
[-4.6] = -4
[-1] = -1
We can see that [x] = 0, when -1 < x ≤ 0
So, we can REPHRASE the target question . . .
REPHRASED target question: Is -1 < x ≤ 0 ?Aside: My video below has tips on rephrasing the target question Statement 1: -1< x< 1 Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = -0.5. In this case, the answer to the REPHRASED target question is
YES, it IS the case that -1 < x ≤ 0Case b: x = 0.5. In this case, the answer to the REPHRASED target question is
NO, it is NOT the case that -1 < x ≤ 0Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x < 0 Let's TEST some values.
There are several values of x that satisfy statement 2. Here are two:
Case a: x = -0.5. In this case, the answer to the REPHRASED target question is
YES, it IS the case that -1 < x ≤ 0Case b: x = -3. In this case, the answer to the REPHRASED target question is
NO, it is NOT the case that -1 < x ≤ 0Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined When we combine the two statements, we get the inequality -1 < x < 0
So, for ALL possible values of x, the answer to the REPHRASED target question is
YES, it IS the case that < x ≤Since we can answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
RELATED VIDEO FROM MY COURSE
If integer is mentioned why do we need to take floating point numbers and round them?
Plus you have written 3.1 = 4, I am sorry but I didnt understand this
I don't believe in giving up!