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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: 5660
If x is an integer and 3x+8>-1, what is the value of x? [#permalink]

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11 Jan 2018, 04:28
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Difficulty:

55% (hard)

Question Stats:

56% (01:16) correct 44% (01:16) wrong based on 71 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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[Reveal] Spoiler: OA

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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, 05:34
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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

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

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15 Jan 2018, 10:47
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.

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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Re: If x is an integer and 3x+8>-1, what is the value of x?   [#permalink] 15 Jan 2018, 10:47
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