Can the experts please help me with this question?
If x is not equal to 0, is |x| less than 1?
a) x/|x|<x
b) |x|>x
Thanks!!
Inequalities
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 48
- Joined: Mon May 23, 2011 9:18 am
- Location: NYC
- Thanked: 17 times
- Followed by:4 members
- GMAT Score:770
Hi safina,
The question essentially asks - is -1<x<1 (excluding 0)?
Choice A: the left hand side will be 1 when x>0 and -1 when x<0. Let's look at the possibilities:
x>1 --> Statement will be TRUE because left hand side is 1 whereas x>1.
0<x<1 --> Statement will be FALSE because left hand side is 1 whereas x is a small positive number
-1<x<0 --> Statement will be TRUE because left hand side is -1 whereas x is a smaller negative number
x<-1: Statement will be FALSE because left hand side is -1 whereas x<-1
Since the statement is TRUE for x>1 and -1<x<0, it is INSUFFICIENT to determine if |x|<1.
Choice B: |x|>x only when x is negative, otherwise they'll be equal. However, this means any negative number would work. So B is INSUFFICIENT on its own.
Together: Test out both cases for choice A being true.
x>1 - makes choice A true but makes choice B false - does not work
-1<x<0 - makes choice A true and choice B true.
Therefore for A and B to be true, -1<x<0 must be true as well. The answer is C
The question essentially asks - is -1<x<1 (excluding 0)?
Choice A: the left hand side will be 1 when x>0 and -1 when x<0. Let's look at the possibilities:
x>1 --> Statement will be TRUE because left hand side is 1 whereas x>1.
0<x<1 --> Statement will be FALSE because left hand side is 1 whereas x is a small positive number
-1<x<0 --> Statement will be TRUE because left hand side is -1 whereas x is a smaller negative number
x<-1: Statement will be FALSE because left hand side is -1 whereas x<-1
Since the statement is TRUE for x>1 and -1<x<0, it is INSUFFICIENT to determine if |x|<1.
Choice B: |x|>x only when x is negative, otherwise they'll be equal. However, this means any negative number would work. So B is INSUFFICIENT on its own.
Together: Test out both cases for choice A being true.
x>1 - makes choice A true but makes choice B false - does not work
-1<x<0 - makes choice A true and choice B true.
Therefore for A and B to be true, -1<x<0 must be true as well. The answer is C
Please feel free to private message me with any questions; I don't check the forums regularly, whereas PMs go straight to my email.
- Bill@VeritasPrep
- GMAT Instructor
- Posts: 1248
- Joined: Thu Mar 29, 2012 2:57 pm
- Location: Everywhere
- Thanked: 503 times
- Followed by:192 members
- GMAT Score:780
I started with Statement 2. If the absolute value of x is greater than the actual value of x, then x must be negative; applying absolute value will make it positive, and a positive is always greater than a negative. However, x could be -1/2 (and we'd say yes to the question) or -10 (and we'd say no), so it is insufficient to say if |x| < 1.safina wrote:Can the experts please help me with this question?
If x is not equal to 0, is |x| less than 1?
a) x/|x|<x
b) |x|>x
Thanks!!
From statement 1:
x/|x| < x
x < x|x|
If x is positive, we have x < x^2, which means x is greater than 1.
If x is negative, it must be between -1 and 0. For instance, -2 < -2(2) does not work, but -1/2 < -1/2 (1/2) does.
The only way to satisfy both statements is for x to between 0 and -1, so its absolute value is always less than 1. Thus, C
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi safina,
This DS question can be beaten by TESTing Values and tracking the results.
We're told that X is CANNOT = 0. We're asked "is |X| < 1?" This is a YES/NO question.
Fact 1: X/|X| < X
Notice the fraction X/|X|; it will only ever equal 1 or -1, depending on the value of X. This also tells us that X COULD be > 1 or it COULD be a negative fraction.
If X = 2 then the answer to the question is NO.
If X = -1/2 then the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: |X| > X
This tells us that X MUST be negative.
If X = -1/2 then the answer to the question is YES.
If X = -2 then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, the only possibility that fits both Facts is that X must be a NEGATIVE FRACTION.
The answer to the question will ALWAYS be YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This DS question can be beaten by TESTing Values and tracking the results.
We're told that X is CANNOT = 0. We're asked "is |X| < 1?" This is a YES/NO question.
Fact 1: X/|X| < X
Notice the fraction X/|X|; it will only ever equal 1 or -1, depending on the value of X. This also tells us that X COULD be > 1 or it COULD be a negative fraction.
If X = 2 then the answer to the question is NO.
If X = -1/2 then the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: |X| > X
This tells us that X MUST be negative.
If X = -1/2 then the answer to the question is YES.
If X = -2 then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, the only possibility that fits both Facts is that X must be a NEGATIVE FRACTION.
The answer to the question will ALWAYS be YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
- Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
Very nice question:
Hope that helps,
-Patrick
Hope that helps,
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.