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.

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