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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x is integer and 3 | x |+x < 4, what is the value of x tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## If x is integer and 3 | x |+x < 4, what is the value of x ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] If x is integer and 3 | x |+x < 4, what is the value of x? 1) x < 0 2) x > -2 _________________ Math Revolution 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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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

If x is integer and 3 | x |+x < 4, what is the value of x?

1) x < 0
2) x > -2
$$3\left| x \right| + x < 4\,\,\,\,\,,\,\,\,\,x\,\,{\mathop{\rm int}}$$
$$? = x$$

$$\left( 1 \right)\,\,\,x < 0\,\,\,\,\, \Rightarrow \,\,\,\,3\left( { - x} \right) + x < 4\,\,\,\,\, \Rightarrow \,\,\,\, - 2x < 4\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\left( { - 2} \right)} \,\,\,\,\,x > - 2$$
$$x > - 2\,\,\,\,\,\,\mathop \Rightarrow \limits^{x\,\,{\mathop{\rm int}} } \,\,\,\,\,\,x = - 1\,\,\,\,\,\left( {x < 0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$

$$\left( 2 \right)\,\,\,x > - 2\,\,\,\left\{ \matrix{ \,\,{\rm{Take}}\,\,x = - 1\,\,\,\,\,\left[ {\,\,3\left| { - 1} \right| + \left( { - 1} \right) < 4\,\,\,} \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,? = - 1\,\, \hfill \cr \,\,{\rm{Take}}\,\,x = 0\,\,\,\,\,\left[ {\,\,3\left| 0 \right| + \left( 0 \right) < 4\,\,\,} \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,? = 0\,\, \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

If x is integer and 3 | x |+x < 4, what is the value of x?

1) x < 0
2) x > -2
3|x| < 4-x

Case 1: Signs unchanged
3x < -x
4x < 4
x < 1

Case 2: Signs changed in the absolute value
3(-x) < 4-x
-2x < 4
x > -2

Question stem, rephrased:
If x is an integer such that -2 < x < 1, what is the value of x?

Statement 1: x < 0
Here, x must be an integer such that -2 < x < 0.
Thus, x = -1.
SUFFICIENT.

Statement 2: x > -2
Statement 2 offers no new information: the prompt itself indicates that - 2 < x < 1,
Since it's possible that x=-1 or that x=0, INSUFFICIENT.

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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. We then recheck the question.

Modifying the original condition:
There are two cases to consider.
Case 1) x ≥ 0:
3|x|+x < 4
=> 3x + x < 4
=> 4x < 4
=> x < 1
=> 0 ≤ x < 1

Case 2) x < 0:
-3x+x < 4
=> -2x < 4
=> x > -2
=> -2 < x <0

Therefore, x is an integer with -2 < x < 1. Thus, the original condition tells us that x = -1 or 0.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since x < 0, we must have x = -1 as the original condition tells us that x = 0 or x = -1.
Condition 1) is sufficient, because it yields a unique solution.

Condition 2)
Both x = 0 and x = -1 satisfy condition 2).
Since it does not yield a unique solution, condition 2) is not sufficient.

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.

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