Last visit was: 03 Jan 2025, 12:10 It is currently 03 Jan 2025, 12:10
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

x ≥ -1 and x ≥ x^5

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
huda
Director
Director
Joined: 22 Jun 2019
Posts: 521
Own Kudos [?]: 726 [0]
Given Kudos: 161
Send PM

Top Member of the Month
x ≥ -1 and x ≥ x^5 [#permalink] New post   Updated on: 21 Jul 2019, 19:18
00:00

Question Stats:

89% (01:51) correct 10% (01:39) wrong based on 19 sessions

Hide Show timer Statistics

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.
avatar
jwolbrum
Intern
Intern
Joined: 21 Jul 2019
Posts: 14
Own Kudos [?]: 32 [2]
Given Kudos: 0
Send PM
Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   Updated on: 22 Jul 2019, 11:04
2
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.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30582
Own Kudos [?]: 36937 [0]
Given Kudos: 26117
Send PM
Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   22 Jul 2019, 02:14
1
Expert Reply
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
avatar
jwolbrum
Intern
Intern
Joined: 21 Jul 2019
Posts: 14
Own Kudos [?]: 32 [0]
Given Kudos: 0
Send PM
Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   22 Jul 2019, 11:03
1
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.
avatar
apokalyptic
Intern
Intern
Joined: 24 Aug 2019
Posts: 14
Own Kudos [?]: 22 [0]
Given Kudos: 0
Send PM
Re: x ≥ -1 and x ≥ x^5 [#permalink] New post   14 Nov 2019, 06:24
1
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
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5089
Own Kudos [?]: 76 [0]
Given Kudos: 0
Send PM
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
gmatclubot
Re: x -1 and x x^5 [#permalink]
17 Apr 2024, 09:51
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1126 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact