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# If x is an integer and 3x+8>-1, what is the value of x?

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Math Expert
Joined: 02 Aug 2009
Posts: 5893
If x is an integer and 3x+8>-1, what is the value of x? [#permalink]

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11 Jan 2018, 05:28
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45% (medium)

Question Stats:

56% (01:21) correct 44% (01:17) wrong based on 93 sessions

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If x is an integer and $$3x+8>-1$$, what is the value of x?

(1) $$x^2*|x|=8$$ .
(2) x^2>1

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Re: If x is an integer and 3x+8>-1, what is the value of x? [#permalink]

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11 Jan 2018, 06:34
1
chetan2u wrote:
If x is an integer and $$3x+8>-1$$, what is the value of x?
(1) $$x^2*|x|=8$$ .
(2) x^2>1

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As all of our information is given in expressions/equations we'll try to work with them.
This is a Precise approach.

We're told that 3x+8 >-1 which simplifies to x > -3.
(1) tells us that x^2 * |x| = 8.
If x is positive, then this simplifies to x^3 = 8 meaning that x = 2.
If x is negative, then this simplifies to -x^3 = 8 meaning that x = -2.
As both 2 and -2 are larger than -3, this is insufficient.

(2) simplifies into x>1 or x<-1.
This still has many possible values of x and so is insufficient.

Combined: (2) does not help us separate between x=2 and x=-2 and is therefore insufficient.

chetan2u I assume the \fraction latex terminology in (1) is a typo?
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Save up to $250 on examPAL packages (special for GMAT Club members) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5585 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x is an integer and 3x+8>-1, what is the value of x? [#permalink] ### Show Tags 15 Jan 2018, 11:47 chetan2u wrote: If x is an integer and $$3x+8>-1$$, what is the value of x? (1) $$x^2*|x|=8$$ . (2) x^2>1 New question 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. $$3x + 8 > -1$$ $$⇔ 3x > -9$$ $$⇔ x > -3$$ Thus the question asks if $$x > -3$$. Since we have 1 variable and 0 equations, D is most likely to be the answer. So, we should consider each of conditions one by one. Condition 1) $$x^2 \cdot |x| = 8$$ $$⇔ |x|^3 = 8$$ $$⇔ |x| = 2$$ $$⇔ x = ±2$$ Since both -2 and 2 are greater than -3, we don't have a unique solution Thus the condition 1) is not sufficient. Condition 2) $$x^2 > 1$$ $$⇔ x^2 - 1 > 0$$ $$⇔ (x+1)(x-1) > 0$$ $$⇔ x < -1$$ or $$x > 1$$ Since -2 and 2 can be solutions, we don't have a unique solution. Thus the condition 2) is not sufficient. Conditions 1) & 2) Since -2 and 2 can be solutions again, we don't have a unique solution. Thus both of the conditions 1) & 2) together are not sufficient. Therefore, the answer is E. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ 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$99 for 3 month Online Course"
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Re: If x is an integer and 3x+8>-1, what is the value of x?   [#permalink] 15 Jan 2018, 11:47
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