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

 It is currently 17 Oct 2019, 04:09

### 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

# Is x|y|=xz?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8009
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

24 Jan 2018, 01:28
00:00

Difficulty:

35% (medium)

Question Stats:

61% (00:59) correct 39% (01:05) wrong based on 117 sessions

### HideShow timer Statistics

[GMAT math practice question]

Is $$x|y|=xz?$$

1) $$x, y,$$ and $$z$$ are positive
2) $$y^2=z^2$$

_________________
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" Senior Manager Joined: 17 Oct 2016 Posts: 313 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: Is x|y|=xz? [#permalink] ### Show Tags 24 Jan 2018, 01:45 C. From Q stem we can decide |y|=z? Statement 1 don't gives much info. in sufficient. Statement 2 says y²=z². At first it may look like this is sufficient. But not. Lets say y=-1 and z=1, this satisfies Q stem as well as st2. But when y=1 and z=-1 Q stem is not satisfied; only st2 is satisfied. Hence st2 is not sufficient alone. Combining, we get, y=1 and z=1 always (although the sign of y doesn't matter). Hence sufficient. This is a Good 'Answer-B trap question'. _________________ Help with kudos if u found the post useful. Thanks Math Expert Joined: 02 Aug 2009 Posts: 7962 Re: Is x|y|=xz? [#permalink] ### Show Tags 24 Jan 2018, 02:41 MathRevolution wrote: [GMAT math practice question] Is $$x|y|=xz?$$ 1) $$x, y,$$ and $$z$$ are positive 2) $$y^2=z^2$$ What do we get from x|y|=xz.. Is x=0 or |y|=z ?.. Sasindran you have missed out on x=0.. 1) x,y and z are positive. So $$x\neq{0}$$, but y can be z, Ans will be yes And if y is NOT EQUAL to z, Ans is NO Insuff 2)y^2=z^2... If z is positive, Ans is yes If z is NEGATIVE, and is NO Insufficient.. Combined z is positive and equal to z.. Ans is yes Sufficient C _________________ Intern Joined: 01 Nov 2017 Posts: 10 Is x|y|=xz? [#permalink] ### Show Tags 24 Jan 2018, 03:35 Additional info for statement 2: x^2=z^2 can be re-written as x^2-z^2=(x+z)(x-z)=0 Now it becomes clear, that there are 2 possible solutions, so we need to check for additional information in statement 1 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8009 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x|y|=xz? [#permalink] ### Show Tags 26 Jan 2018, 01:16 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. Modifying the question: $$x|y| = xz$$ $$⇔ x(|y|-z) = 0$$ $$⇔ x = 0$$ or $$|y| = z$$ $$⇔ x = 0$$ or $$y = z$$ or $$y = -z$$ Since we have 3 variables ($$x, y,$$ and $$z$$) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. Conditions 1) & 2): Condition 2) tells us that $$y = z$$or $$y = -z$$. Since condition 1) states that $$x, y, z > 0$$, we can only have $$y = z$$. Thus, both conditions are sufficient, when taken together. Therefore, the answer is C. In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D. Answer: C _________________ 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"
Re: Is x|y|=xz?   [#permalink] 26 Jan 2018, 01:16
Display posts from previous: Sort by