GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 05:26

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

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

Absolute Values

Author Message
Intern
Joined: 12 Jun 2015
Posts: 7
Concentration: General Management
GMAT Date: 09-08-2015
GPA: 3.55
WE: Account Management (Manufacturing)

Show Tags

20 Mar 2017, 08:18
hi Guys,

I wanted to know why in the attached screen shot the answer is x*2 = X*2

thanks
Attachments

Untitled.jpg [ 154.78 KiB | Viewed 482 times ]

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82

Show Tags

22 Mar 2017, 12:50
jamescarey86 wrote:
hi Guys,

I wanted to know why in the attached screen shot the answer is x*2 = X*2

thanks

$$\frac{x}{|y|} = -1$$ is equivalent to $$x = -|y|$$ or $$-x = |y|$$.
It is also equivalent to $$(-x)^2 = |y|^2 = y^2$$, and so we have $$x^2 = y^2$$.
Hence, D is the correct answer.

We have used a property as follows.
- $$|x| = a$$ is equivalent to $$x^2 = a^2$$.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Joined: 30 Nov 2015
Posts: 33
Location: United States (CO)
WE: Information Technology (Consumer Products)

Show Tags

23 Sep 2019, 20:23
I always forget the properties of absolute values and so I always go by the basics. Any value inside mods can come out as +ve or -ve.

x / |y| can be either x/y or x/-y.

so,
x/y = -1
Which means x = -y

or

x/-y = -1 which can be written as x/y = 1 and ultimately, x = y.

Now looking at x = -y and x = y, the only way to make them equal is by squaring both the equations. -y square will be positive and equal to the square of y. Hence answer is D.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170

Show Tags

24 Sep 2019, 14:04
Hi All,

We're told that X/|Y| = -1. We're asked which of the following MUST be true (which really means "which of the following is ALWAYS true no matter how many different examples you come up with?"). This question can be solved by TESTing VALUES.

For a fraction to equal -1, the numerator and denominator must be OPPOSITE values: for example, -2 and +2. In this fraction, the denominator is an Absolute Value, so there's no way for the denominator to be negative. Thus, the numerator MUST be negative. Based on that deduction, there are now 2 possibilities:

1) X is negative and Y is positive
2) X is negative and Y is negative (and that negative value will be made positive by the Absolute Value function).

So, which of the 5 answers is ALWAYS true (both when X = -2, Y = +2 AND when X = -2 and Y = -2)? Only one...

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: Absolute Values   [#permalink] 24 Sep 2019, 14:04
Display posts from previous: Sort by

Absolute Values

Moderator: souvonik2k