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x ≥ -1 and x ≥ x^5

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huda
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x ≥ -1 and x ≥ x^5 [#permalink] New post   Updated on: 21 Jul 2019, 19:18
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If \(x ≥ -1\) and \(x ≥ x^5\) which of the following must be the correct answer?

A. \(x > 1\)
B. \(0 < x < 1\)
C. \(0 ≥ x ≥ -1\)
D. \(x > 0\)
E. None of these.

Show: :: OA
Actually I don't know the answer. :) In my opinion, it will be E. You are welcome to try. :wink:

Originally posted by huda on 21 Jul 2019, 15:19.
Last edited by huda on 21 Jul 2019, 19:18, edited 1 time in total.
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jwolbrum
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Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   Updated on: 22 Jul 2019, 11:04
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I've placed spoiler tags in case you want to work out the answer with a little nudging rather than a lot.

It's always a good idea to start with the bottom and/or the top of a given range. What is the smallest possible legal value for x? Let's test that and see if we can knock out any answers.

Show: :: Testing our smallest legal value.
If x = -1, both the left and right inequality will hold, so -1 can be a viable option. That's enough to eliminate A, B, and D all by itself.


Show: :: Dealing with the remaining choices.
If we can find a case where x can be greater than 0, then we can also eliminate answer choice C. The simplest value to test is 1, and that will also work, so C cannot be correct. The answer is E.


A more comprehensive way to solve this problem would be to identify what specific values satisfy both inequalities.

Show: :: For which values does the right inequality hold?
The values of -1, 0, and 1 all work.
If x is less than -1, raising it to the fifth power will give us a smaller number. (Try -2.)
If x is between 0 and 1, raising it to the fifth power will give us a smaller number. (Try -\(\frac{1}{2}\).)

Combined with the left inequality, our legal values for x are now -1 and \(1 ≥ x ≥ -0\).


-Jordan Wolbrum

Originally posted by jwolbrum on 21 Jul 2019, 18:54.
Last edited by jwolbrum on 22 Jul 2019, 11:04, edited 1 time in total.
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Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   22 Jul 2019, 02:14
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Hi,

your explanation is quite good. However, I do not understand the meaning of usage of the spoiler tag and not a straight explanation.

regards
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jwolbrum
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Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   22 Jul 2019, 11:03
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Carcass wrote:
Hi,

your explanation is quite good. However, I do not understand the meaning of usage of the spoiler tag and not a straight explanation.

regards


I wanted to give readers the opportunity to solve on their own with gentle hints before giving the answer. That's generally how I would teach that problem in a tutoring session.

However, when I kept reading posts, I realized I was the only one doing that, so now I'd limit that to weird solutions or additional thoughts about a question on this forum.
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Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   14 Nov 2019, 06:24
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The answer is B.

The key word is must be. i.e equation holds true for all values of x in the range.
x≥−1
x≥x5
Checking x = 0 , T T
Checking x=1 , T T
Checking x= -1, T T
Checking x=2, T F -- option A,D is eliminated
Checking x= 1/2 , T T
Checking x=-1/2 ,T F -- option C is eliminated

B holds true
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Re: x -1 and x x^5 [#permalink] New post   17 Apr 2024, 09:51
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: x -1 and x x^5 [#permalink]
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