KarishmaB wrote:
corvinis wrote:
If |x| > 3, which of the following must be true?
I. x > 3
II. X^2 > 9
III. |x-1|>2
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I can't understand how the official answer can be right. For me is B. Please respond and I'll provide official explanation! Thanks
Responding to a pm:
|x| > 3 implies that x is a point whose distance from 0 is more than 3. So x could be greater than 3 or less than -3. Before you move further, think about the values x can take: 3.00001, 3.5, 4.2, 5.7, 67, 1000, -3.45, -4, -8, -100 etc. The only values it cannot take are -3 <= x <= 3
Which of the following must be true?
I. x > 3
For every value that x can take, must x be greater than 3? No. e.g. if x takes -3.45, -4 etc, it will not be greater than 3 so this is not true.
II. X^2 > 9
This is the same as |x| > 3 so it must be true
III. |x-1|>2
This implies that the distance of x from 1 must be greater than 2. So x is either greater than 3 or less than -1. Now, recall all the values that x can take. For each value, can be say that x is either greater than 3 or less than -1? Yes.
3.00001 - x is greater than 3
3.5 : x is greater than 3
4.2 : x is greater than 3
5.7 : x is greater than 3
67 : x is greater than 3
1000 : x is greater than 3
-3.45 : x is less than -1
-4 : x is less than -1
-8 : x is less than -1
-100 : x is less than -1
For every value that x can take, x will be either greater than 3 or less than -1. Note that we are not saying that every value less than -1 must be valid for x. We are saying that every value that is valid for x (found by using |x| > 3) will be either greater than 3 or less than -1. Hence |x-1|>2 must be true for every value that x can take.
Hi
KarishmaB, I have a few doubts regarding this question and other it's variations.
I understood that for |x| > 3 to be true x <-3 or x> 3 i.e. x = -3.1 , -4 , 4 , 4.1. and so on, but not 3,-3, -2, -1 etc.
Now, in (I) x > 3, why is this not a must be true statement?. How do we differentiate between must be / could be true where we have 2 applicable ranges for the question stem.
Per my understanding, x>3 will always be true for the given question stem because whatever value x>3 gives, it will always satisfy |x| > 3
In (III) we get the range for |x-1| > 2, as x <-1 or x>3,
x>3 satisfies the question stem, but I don't see how x <-1 satisfies it.
What if x takes the value -2 ? in that case |-2| >/ 3.
How is this a must be true scenario. All the values from -1 to -3 inclusive will fail the question stem.
Could you please point out where I'm going wrong? I'm almost always incorrect on questions of this form.