Which of the following describes all values of x for which 1-x^2 ≥ 0 ?
A. x ≥ 1
B. x ≤ -1
C. 0 ≤ x ≤ 1
D. x ≤ -1 or x ≥ 1
E. -1 ≤ x ≤ 1
Answer - Option E
Thanks
Bullzi
Inequalities - Values of x
This topic has expert replies
Now, though I got the corect answer, I wanted to check if my approach is correct
1. 1-x^2>=0
2. -x^2>=-1
3. x^2<=1
4. Taking square root both sides, x<= (+-1)
5. x<= (+-1) can be written as [spoiler]-1<=x<=1[/spoiler], hence option E
Thanks
Bullzi
1. 1-x^2>=0
2. -x^2>=-1
3. x^2<=1
4. Taking square root both sides, x<= (+-1)
5. x<= (+-1) can be written as [spoiler]-1<=x<=1[/spoiler], hence option E
Thanks
Bullzi
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It is possible that x = 1/2, since 1 - (1/2)² ≥ 0.Bullzi wrote:Which of the following describes all values of x for which 1-x^2 ≥ 0 ?
A. x ≥ 1
B. x ≤ -1
C. 0 ≤ x ≤ 1
D. x ≤ -1 or x ≥ 1
E. -1 ≤ x ≤ 1
Eliminate any answer choice that does not include x = 1/2 within its range.
Eliminate A, B and D.
It is possible that x = -1/2, since 1 - (-1/2)² ≥ 0.
Eliminate C, since it does not include x = -1/2 within its range.
The correct answer is E.
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Hi Bullzi,
With inequality-based questions, sometimes the easiest approach is just to come up with a few examples that 'fit' the given prompt and then use those examples to eliminate answer choices.
Here, we're told that 1 - X^2 >= 0. We're asked for ALL of the possible values that fit this inequality.
The 'easiest' value that most Test Takers would immediately 'see' is 1 (since 1 - 1^2 = 0), so X COULD be 1.
Next, since we're dealing with a squared term, -1 would also be a solution (since 1 - [-1]^2 = 0).
So we immediately have at least two solutions: 1 and -1. We can eliminate Answers A, B and C.
For the last step, we have to determine what OTHER solutions are possible. You can either prove that fractions fit (try using X = 1/2) or proving that larger integers do NOT fit (try using X = 2). Either way, you can eliminate the final incorrect answer.
Final Answer: E
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Rich
With inequality-based questions, sometimes the easiest approach is just to come up with a few examples that 'fit' the given prompt and then use those examples to eliminate answer choices.
Here, we're told that 1 - X^2 >= 0. We're asked for ALL of the possible values that fit this inequality.
The 'easiest' value that most Test Takers would immediately 'see' is 1 (since 1 - 1^2 = 0), so X COULD be 1.
Next, since we're dealing with a squared term, -1 would also be a solution (since 1 - [-1]^2 = 0).
So we immediately have at least two solutions: 1 and -1. We can eliminate Answers A, B and C.
For the last step, we have to determine what OTHER solutions are possible. You can either prove that fractions fit (try using X = 1/2) or proving that larger integers do NOT fit (try using X = 2). Either way, you can eliminate the final incorrect answer.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
\GMATGuruNY wrote:It is possible that x = 1/2, since 1 - (1/2)² ≥ 0.Bullzi wrote:Which of the following describes all values of x for which 1-x^2 ≥ 0 ?
A. x ≥ 1
B. x ≤ -1
C. 0 ≤ x ≤ 1
D. x ≤ -1 or x ≥ 1
E. -1 ≤ x ≤ 1
Eliminate any answer choice that does not include x = 1/2 within its range.
Eliminate A, B and D.
It is possible that x = -1/2, since 1 - (-1/2)² ≥ 0.
Eliminate C, since it does not include x = -1/2 within its range.
The correct answer is E.
Nicely explained.
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Bullzi wrote:Which of the following describes all values of x for which 1-x^2 ≥ 0 ?
A. x ≥ 1
B. x ≤ -1
C. 0 ≤ x ≤ 1
D. x ≤ -1 or x ≥ 1
E. -1 ≤ x ≤ 1
Simplifying we have:
1 ≥ x^2
√1 ≥ √x^2
1 ≥ |x|
Now we solve for x:
When x is positive:
1 ≥ |x|
1 ≥ x
x ≤ 1
This can be re-expressed as x ≤ 1.
When x is negative:
1 ≥ |x|
1 ≥ -x
-1 ≤ x
We combine the two resulting inequalities to get:
-1 ≤ x ≤ 1
Answer: E
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