What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25

Answer is E.

(i) simplifying the equation, (x+4)(x-3)=0 ; x=-4 or 3 Not sufficient.
(ii) X^2 <25 that implies, x=2,3,4 etc., Not sufficient.

Combining (i) and (ii), still not enough data to find value of x. Not sufficient. thus, answer is E

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 of the conditions on their own first.

Condition 1)
x^2 +x-12 = 0
⇔ (x-3)(x+4) = 0
⇔ x = 3 or x = -4

Since we don't have a unique solution, the condition 1) is not sufficient.

Condition 2)
x^2 < 25
⇔ -5 < x < 5

Since we don't have a unique solution, the condition 2) is not sufficient.

Condition 1) & 2)
Since x = 3 or x = -4 from the condition 1) and -5 < x < 5 from the condition 2), we have x = 3 or x = -4.
Since we don't have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

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.

Answer is E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I) X= -4 or 3
Insufficient

II)x=-4 to +4
Insufficient
Combining
Multiple values so answer is E

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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.

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

Condition 1)
x^2 + x - 12 = 0
⇔ (x+3)(x-4) = 0
⇔ x = -3 or x = 4

Since we don't have a unique solution, the condition 1) is not sufficient.

Condition 2)
x^2 < 25
⇔ x^2 - 25 < 0
⇔ (x+5)(x-5) < 0
⇔ -5 < x < 5

Since we don't have a unique solution, the condition 2) is not sufficient.

Conditions 1) & 2)

We have x = -3 or x = 4 from the condition 1).
We have -5 < x < 5, from the condition 2).
Even when we consider both conditions together, we have x = -3 or x = 4.

Since we don't have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

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.