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# If x is an integer and |x|+(x/3)<5, what is the value of x?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink]

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18 Dec 2017, 00:24
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Difficulty:

65% (hard)

Question Stats:

48% (01:40) correct 52% (01:33) wrong based on 29 sessions

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[GMAT math practice question]

If $$x$$ is an integer and $$|x|+(\frac{x}{3})<5$$, what is the value of $$x$$?

1) $$x>-12$$
2) $$x<-6$$
[Reveal] Spoiler: OA

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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 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5776 If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink] ### Show Tags 18 Dec 2017, 00:54 MathRevolution wrote: [GMAT math practice question] If $$x$$ is an integer and $$|x|+(\frac{x}{3})<5$$, what is the value of $$x$$? 1) $$x>-12$$ 2) $$x<-6$$ Let's solve the equation.. $$|x|+(\frac{x}{3})<5......3|x|+x<5$$, So .. A) 3x+x<15.....4x<15.....x<15/4 B) -3x+x<15.....-2x<15.....2x>-15....x> -15/2....x>-7.5 So the question basically gives the value of x between -7.5 and 15/4 Let's see what each statement tells us 1) x>-12 x could be -7,-6,....0,1,2,3 Insufficient 2) x<-6 x=-7..YES So ans -7 Sufficient B Edited.. mixed two Qs _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Senior Manager Joined: 05 Dec 2016 Posts: 260 Concentration: Strategy, Finance GMAT 1: 620 Q46 V29 Re: If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink] ### Show Tags 18 Dec 2017, 01:42 Solving the inequality we get the following possible values for x: -7,5<x<3,75 Taken that x is an integer we get -7<=x<=3 (1) x>-12 x can be -7;-6.....3 (2) x<-6 Taken that limit, only one integer conforms to it, x=-7 Answer B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5269 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink] ### Show Tags 20 Dec 2017, 01:50 => 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 VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations. Modifying the original condition: There are two cases to consider. Case 1) $$x ≥ 0$$ $$|x|+(\frac{x}{3})<5$$ $$⇔ x + \frac{x}{3} < 5$$ $$⇔ (\frac{4}{3})x < 5$$ $$⇔ x < \frac{15}{4}$$ $$⇔ x = 0, 1, 2, 3$$ Case 2) $$x < 0$$ $$|x|+(\frac{x}{3})<5$$ $$⇔ -x + \frac{x}{3} < 5$$ $$⇔ -(\frac{2}{3})x <5$$ $$⇔ x > \frac{-15}{2}$$ $$⇔ x > -7.5$$ $$⇔ x = -7, -6, -5, -4, -3, -2 or -1$$ The question asks for the value of $$x$$ if $$x$$ is one of $$-7, -6, -5, …, 0, 1, 2, 3$$. Since we have 1 variable (x), D is most likely to be the answer. Condition 1) All of the possible values of $$x$$ are greater than $$-12$$. Therefore, we do not have a unique solution, and this condition is not sufficient. Condition 2) The only possible value of $$x$$ is $$-7$$. Since we have a unique solution, condition 2) is sufficient. Therefore, B is the answer. Answer: B _________________ 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 3 month Online Course"
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Re: If x is an integer and |x|+(x/3)<5, what is the value of x?   [#permalink] 20 Dec 2017, 01:50
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