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Inequalities - Values of x

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by Bullzi » Fri Oct 02, 2015 11:56 pm
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

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by Bullzi » Fri Oct 02, 2015 11:58 pm
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

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by GMATGuruNY » Sat Oct 03, 2015 2:43 am
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
It is possible that x = 1/2, since 1 - (1/2)² ≥ 0.
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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by [email protected] » Sat Oct 03, 2015 9:00 am
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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by gmat_boss » Sat Oct 03, 2015 8:34 pm
GMATGuruNY wrote:
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
It is possible that x = 1/2, since 1 - (1/2)² ≥ 0.
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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by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:37 pm
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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Head of GMAT Instruction
[email protected]

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