It is currently 23 Sep 2020, 01:56
My Tests

Close

GMAT 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 GMAT 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.

x is an integer such that –x|x| ≥ 4.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 13344
Followers: 288

Kudos [?]: 3381 [1] , given: 12176

CAT Tests
x is an integer such that –x|x| ≥ 4. [#permalink] New post 08 Aug 2018, 16:37
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

65% (00:45) correct 34% (00:58) wrong based on 145 sessions
x is an integer such that \(- x|x| ≥ 4\).

Quantity A
Quantity B
x
2


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

1 KUDOS received
Manager
Manager
User avatar
Joined: 06 Jun 2018
Posts: 94
Followers: 2

Kudos [?]: 77 [1] , given: 0

Re: x is an integer such that –x|x| ≥ 4. [#permalink] New post 09 Aug 2018, 15:15
1
This post received
KUDOS
Carcass wrote:
x is an integer such that \(- x|x| ≥ 4\).

Quantity A
Quantity B
x
2


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E



Given

\(- x|x| ≥ 4\)

Note:

|x| is always positive.

we have a negative sign with x but ultimate value is positive. So x have to be negative. Negative times negative is positive.

The best answer is B. 2 is greater than x, a negative integer.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 176 [0], given: 4

Re: x is an integer such that –x|x| ≥ 4. [#permalink] New post 23 Oct 2018, 03:02
Expert's post
Carcass wrote:
x is an integer such that \(- x|x| ≥ 4\).

Quantity A
Quantity B
x
2


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E


Now \(- x|x| ≥ 4\) which means \(- x|x| > 0\) which is possible when both -x and |x| have same sign. |x|>0 so -x>0...
Multiply the sides if equation by '-', so -(-x)<-(0)...x<0

Since x<0, x has to be less than 2..
Thus B>A

B
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Manager
Manager
Joined: 23 Oct 2018
Posts: 57
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: x is an integer such that –x|x| ≥ 4. [#permalink] New post 23 Oct 2018, 08:41
it was interesting.
Intern
Intern
Joined: 24 Sep 2018
Posts: 32
Followers: 0

Kudos [?]: 45 [0], given: 2

Re: x is an integer such that –x|x| ≥ 4. [#permalink] New post 23 Oct 2018, 20:00
Divide both sides by -x gives you |x| (< or =) 4/-x noting that you will be flipping the direction of the greater than sign since you are dividing by a negative. While you can then go and solve as you would any absolute value, having isolated the absolute value onto one side at this point, you can also see that the only way for the absolute value to be equal to a positive number (absolute values cannot be negative) is if the x value itself is negative. Since any negative number (x > 0) is going to be less than 2, we know that the answer will be B.
1 KUDOS received
Director
Director
User avatar
Joined: 22 Jun 2019
Posts: 517
Followers: 4

Kudos [?]: 104 [1] , given: 161

CAT Tests
Re: x is an integer such that –x|x| ≥ 4. [#permalink] New post 05 Jul 2019, 04:25
1
This post received
KUDOS
Carcass wrote:
x is an integer such that \(- x|x| ≥ 4\).

Quantity A
Quantity B
x
2


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E


Need a better explanation.
_________________

New to the GRE, and GRE CLUB Forum?
GRE: All About GRE | Search GRE Specific Questions | Download Vault
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection
Books: All GRE Best Books
Scores: Average GRE Score Required By Universities in the USA
Tests: All Free & Paid Practice Tests | GRE Prep Club Tests
Extra: Permutations, and Combination
Vocab: GRE Vocabulary
Facebook GRE Prep Group: Click here to join FB GRE Prep Group

2 KUDOS received
Intern
Intern
Joined: 15 Jul 2020
Posts: 2
Followers: 0

Kudos [?]: 3 [2] , given: 0

Re: x is an integer such that –x|x| ≥ 4. [#permalink] New post 15 Jul 2020, 10:46
2
This post received
KUDOS
A more human-like approach:

1. You first try to solve it conventionally, but quickly find out that it's not the right method.
−x(x)≥4 and −x(-x)≥4 lead to no good answer.

2. You then analyze it logically like how chetan2u explained.
-x|x| must be positive; the element |x| is always positive; so the element -x must become positive. Thus, x must be negative so the answer is B.
Re: x is an integer such that –x|x| ≥ 4.   [#permalink] 15 Jul 2020, 10:46
Display posts from previous: Sort by

x is an integer such that –x|x| ≥ 4.

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.