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

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

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13 Apr 2018, 02:17
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What is the value of x?

(1) x^2 + x - 12 = 0
(2) x^2 < 25

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Joined: 28 Apr 2014
Posts: 52
GMAT 1: 640 Q50 V25
Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25  [#permalink]

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13 Apr 2018, 02:29
IMO E

St1
x=4,-3
insufficient

St2
-5<x<5
insufficient

Combining, no unique value of x
insufficient
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Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25  [#permalink]

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13 Apr 2018, 02:30
Bunuel wrote:
What is the value of x?

(1) x^2 + x - 12 = 0
(2) x^2 < 25

(1) $$x^2 + x - 12 = 0$$
$$x^2 + 4x - 3x -12 = 0$$
$$(x +4) (x - 3) = 0$$

x = -4 or 3
Hence Insufficient

(2) $$x^2 < 25$$
x^2 - 5^2 < 0
(x + 5)(x - 5) < 0

x = (-5,5)
Hence Insuff

(1) + (2) : x could be either -4 or 3.
Hence insuff

Hence Option (E) is our answer.

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Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25  [#permalink]

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13 Apr 2018, 12:33

(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
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Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25  [#permalink]

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16 Apr 2018, 08:05
Bunuel wrote:
What is the value of x?

(1) x^2 + x - 12 = 0
(2) x^2 < 25

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.
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 04 May 2014 Posts: 22 Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25 [#permalink] Show Tags 16 Apr 2018, 08:32 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. Director Joined: 02 Oct 2017 Posts: 601 Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25 [#permalink] Show Tags 28 Apr 2018, 09:45 I) X= -4 or 3 Insufficient II)x=-4 to +4 Insufficient Combining Multiple values so answer is E Posted from my mobile device Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5866 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25 [#permalink] Show Tags 30 Apr 2018, 12:46 Bunuel wrote: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: What is the value of x? (1) x^2 + x - 12 = 0 (2) x^2 < 25 &nbs [#permalink] 30 Apr 2018, 12:46
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