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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
Posts: 4705
GPA: 3.82
If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink]

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17 Dec 2017, 23:24
00:00

Difficulty:

75% (hard)

Question Stats:

46% (01:34) correct 54% (01:33) wrong based on 28 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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Joined: 02 Aug 2009
Posts: 5537
If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink]

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17 Dec 2017, 23:54
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
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Re: If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink]

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18 Dec 2017, 00:42
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

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82
Re: If x is an integer and |x|+(x/3)<5, what is the value of x? [#permalink]

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20 Dec 2017, 00:50
=>

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.

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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, 00:50
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