Data Sufficiency

[GMAT math practice question]

$$Is\ x>0?$$

$$1)\ x^3+x^2+x=1$$
$$2)\ x^2-4x-5>0$$

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

$$Is\ x>0?$$

$$1)\ x^3+x^2+x=1$$
$$2)\ x^2-4x-5>0$$

In Statement 1, the only real solution is x ≈ 1/2, but Statement 2 requires that x<-1 or x>5.
Since the two statements contradict each other, the problem is invalid.

=>
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.

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):
x^3+x^2+x = 1
=> x(x^2+x+1) = 1
=> x = 1 / (x^2+x+1)
=> x = 1 / (x^2+x+1) > 0 since x^2+x+1 > 0.

Thus, condition 1) is sufficient.


Condition 2):
x^2 - 4x -5 > 0
=> (x+1)(x-5) > 0
=> x < 1 or x > 5

Since the solution set of the inequality, x > 0, from the question does not include the solution set of the inequality from condition 2), x < 1 or x > 5, condition 2) is not sufficient.


Therefore, A is the answer.

Answer: A

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.