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• ### $450 Tuition Credit & Official CAT Packs FREE February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT practice February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST Instead of wasting 3 months solving 5,000+ random GMAT questions, focus on just the 1,500 you need. # Is x/yz>0？  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 Is x/yz>0？ [#permalink] ### Show Tags 27 Mar 2018, 01:17 00:00 Difficulty: 35% (medium) Question Stats: 74% (01:50) correct 26% (01:51) wrong based on 47 sessions ### HideShow timer Statistics [GMAT math practice question] Is $$\frac{x}{yz}>0$$？ $$1) yz>x^2$$ $$2) x<y+z$$ _________________ 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$149 for 3 month Online Course"
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Joined: 21 Aug 2013
Posts: 1431
Location: India

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27 Mar 2018, 05:41
MathRevolution wrote:
[GMAT math practice question]

Is $$\frac{x}{yz}>0$$？

$$1) yz>x^2$$
$$2) x<y+z$$

x/yz will be > 0 if signs of both 'x' and 'yz' are same, i.e., either both are positive or both are negative.

Statement 1:
If yz > x^2 then yz has to be positive (because square of x can not be negative).
But sign of x is not given. So we cannot conclude. Not sufficient.

Statement 2:
x < y+z. This doesnt tell anything about signs of y, z or x. Not sufficient.

Combining the statements:
yz is positive so either both y/z are positive, or both y/z are negative.
Lets take the case of y=3, z=2. Here yz =6 and y+z = 5. Now, as per the two statements:

x^2 < 6 and x < 5. Lets take x=2, it satisfies both. And we can also take x=-1, it also satisfies both. But in first case, x/yz will be positive while in second case x/yz will be negative. So not sufficient, since we cannot determine the sign of x/yz.

Intern
Joined: 16 Apr 2015
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27 Mar 2018, 17:58
MathRevolution wrote:
[GMAT math practice question]

Is $$\frac{x}{yz}>0$$？

$$1) yz>x^2$$
$$2) x<y+z$$

I have question for solution proposed here, from $$yx> x^2$$, we know yz is positive since value of $$x^2$$ can never be negative. We know at this point that y & z have same sign.
This also follows

$$xyz > 0$$ we can multiply yz on both sides since multiplying +ve number on both side of in-equality will not chnage the sign. This would mean xyz >0 can only hold trye if and only if x is +ve, as only +ve * +ve results in >0.

Please let me know if I am over extending the problem
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6949
GMAT 1: 760 Q51 V42
GPA: 3.82

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29 Mar 2018, 00:08
=>

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.

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. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2) together:
If $$x = 1, y = 2$$ and $$z = 3$$, then the answer is ‘yes’.
If $$x = -1, y = 2$$ and $$z = 3$$, then the answer is ‘no’.

Since we don’t have a unique answer, both conditions together are not sufficient.

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x/yz>0？ [#permalink] ### Show Tags 03 Apr 2018, 21:49 sameerspice wrote: MathRevolution wrote: [GMAT math practice question] Is $$\frac{x}{yz}>0$$？ $$1) yz>x^2$$ $$2) x<y+z$$ I have question for solution proposed here, from $$yx> x^2$$, we know yz is positive since value of $$x^2$$ can never be negative. We know at this point that y & z have same sign. This also follows $$xyz > 0$$ we can multiply yz on both sides since multiplying +ve number on both side of in-equality will not chnage the sign. This would mean xyz >0 can only hold trye if and only if x is +ve, as only +ve * +ve results in >0. Please let me know if I am over extending the problem You are talking about the condition 1) only. It is valid for the condition 1). It not over-extending. Depending on x, x/yz could be positive or negative. Thus the condition 1) only is not sufficient. If you consider the condition 2), the above description is not valid. _________________ 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$149 for 3 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/yz>0？   [#permalink] 03 Apr 2018, 21:49
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