X / |X| < X

Expert replies

uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Mon Oct 05, 2009 6:49 pm

X / |X| < X . Which of the following must be true about integer X ? X is not equal to 0.

A X > 1
B X > -1
C |X| < 1
D |X| = 1
E |X|^2 > 1

LOST!! :roll:

Like this post

Source: Beat The GMAT — Problem Solving | Mon Oct 05, 2009 6:49 pm

xcusemeplz2009: Master | Next Rank: 500 Posts; Posts: 399; Joined: Wed Apr 15, 2009 3:48 am; Location: india; Thanked: 39 times

by xcusemeplz2009 » Tue Oct 06, 2009 3:26 am

IMO A

It does not matter how many times you get knocked down , but how many times you get up

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: X / |X| < X

by Stuart@KaplanGMAT » Tue Oct 06, 2009 2:29 pm

uptowngirl92 wrote:X / |X| < X . Which of the following must be true about integer X ? X is not equal to 0.

A X > 1
B X > -1
C |X| < 1
D |X| = 1
E |X|^2 > 1

LOST!! :roll:

We know that x doesn't equal 0. So let's break it down into the two other possible cases:

x>0 and x<0

If x is positive, then |x| = x and we can simplify:

x/x < x

1 < x

So, if x is positive, x must be greater than 1.

If x is negative, then |x| = -x (since a negative times a negative gives us a positive) and we can simplify:

x/-x < x

-1 < x

However, we know that x must be an integer (because that's what the question tells us). Since there are no negative integers greater than -1, there are no possible negative values for x.

Accordingly, we can ignore the x < 0 case. Since x must be postive, x must be greater than 1: choose A.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

sanjana: Master | Next Rank: 500 Posts; Posts: 182; Joined: Sun Aug 02, 2009 7:19 pm; Thanked: 18 times; GMAT Score:680

by sanjana » Wed Oct 07, 2009 1:59 am

Stuart,

I didnt understand this bit,
"Since there are no negative integers greater than -1, there are no possible negative values for x. "

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed Oct 07, 2009 10:16 am

sanjana wrote:Stuart,

I didnt understand this bit,
"Since there are no negative integers greater than -1, there are no possible negative values for x. "

We were looking at the case in which x is negative.

Based on our math, we know that:

x > -1

Well, if x is negative and x > -1, then:

-1 < x < 0,

i.e. x is a negative fraction.

So, in order for x to be negative we have to meet two conditions: x must be an integer and x must be a fraction; since no numbers meet both of those conditions, there are no possible negative values of x.

Like this post

mohit11: Master | Next Rank: 500 Posts; Posts: 293; Joined: Thu Jan 14, 2010 9:08 amFollowed by: 5 members; Location: India; Thanked: 36 times; GMAT Score:730

by mohit11 » Wed Aug 11, 2010 7:56 am

X / |X| < X . Which of the following must be true about integer X ? X is not equal to 0.

A X > 1
B X > -1
C |X| < 1
D |X| = 1
E |X|^2 > 1

I still don't understand. X = |X| * |X| therefore, X/|X| = |X|

Equation says, |X| < X , So we can consider 3 cases, X = 0, -1 and 1

When X = 0 , LHS = RHS , therefore, not true
When X = 1 or X >0 , LHS = RHS , not true
When X=-1 or x <0, LHS >RHS, which is contrary to whats given in the question, therefore, not true.

I don't think the relation given in the question can hold true. If We go by the answer provided by Stuart, X>1, consider X = 2

LHS = 2 , RHS = 2 , not true...

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review