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# If x^2-3x=10, what is the value of x?

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Math Revolution GMAT Instructor
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If x^2-3x=10, what is the value of x?  [#permalink]

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08 Oct 2018, 00:54
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[Math Revolution GMAT math practice question]

If $$x^2-3x=10$$, what is the value of $$x$$?

$$1) x^2-4 = 0$$
$$2) x<6$$

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" examPAL Representative Joined: 07 Dec 2017 Posts: 889 Re: If x^2-3x=10, what is the value of x? [#permalink] ### Show Tags 08 Oct 2018, 01:07 The answer is A. As with many DS questions, we can use the LOGICAL approach to save time here: the information in the question, a quadratic equation, will give us two possible values for x. 1) this, another quadratic equation, will give us two answers as well. We will find the overlap between the two sets of answers - and end up with one answer! sufficient! 2) here we have no choice but to go back and solve the original equation: x2−3x=10 ==> x^2-3x-10=o ==> (x-5)(x+2)=0 ==> x=5, -2. Since BOTH of these values are smaller than 6, this statement doesn't help us - insufficient! _________________ Director Joined: 19 Oct 2013 Posts: 508 Location: Kuwait GPA: 3.2 WE: Engineering (Real Estate) Re: If x^2-3x=10, what is the value of x? [#permalink] ### Show Tags 08 Oct 2018, 01:12 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x^2-3x=10$$, what is the value of $$x$$? $$1) x^2-4 = 0$$ $$2) x<6$$ from question stem x is -2 or 5 1) x = -2 or 2 Sufficient as it satisfies the question stem. With a unique value. 2) x = -2 or 5 insufficient 2 different values that satisfy the question stem. Answer choice A Posted from my mobile device Director Joined: 18 Jul 2018 Posts: 675 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: If x^2-3x=10, what is the value of x? [#permalink] ### Show Tags 08 Oct 2018, 01:13 Solving the question stem. x^2-3x-10 = 0. Gives x as 5 or -2. From statement 1: x^2 = 4. Or x = +2 or -2. So x will be -2. Sufficient. From statement 2: x<6. Both 5 and -2 are less than 6. Hence so unique value. Insufficient. A is the answer Posted from my mobile device _________________ Press +1 Kudo If my post helps! CEO Joined: 11 Sep 2015 Posts: 3437 Location: Canada Re: If x^2-3x=10, what is the value of x? [#permalink] ### Show Tags 08 Oct 2018, 05:46 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x^2-3x=10$$, what is the value of $$x$$? $$1) x^2-4 = 0$$ $$2) x<6$$ Given: x² - 3x = 10 Subtract 10 from both sides to get: x² - 3x - 10 = 0 Factor: (x - 5)(x + 2) = 0 So, EITHER x = 5 OR x = -2 Target question: What is the value of x? Statement 1: x² - 4 = 0 Factor: (x + 2)(x - 2) = 0 So, EITHER x = -2 OR x = 2 When we combine this with the fact that EITHER x = 5 OR x = -2, we can see that x must equal -2 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: x < 6 We already determined that EITHER x = 5 OR x = -2 Since 5 and -2 are each less than 6, statement 2 doesn't help us. It COULD be the case that x = 5 or it COULD be the case that x = -2 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6967 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x^2-3x=10, what is the value of x? [#permalink] ### Show Tags 09 Oct 2018, 23:56 => 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. We then recheck the question. The original condition $$x^2-3x=10$$ is equivalent to $$x = -2$$ or $$x = 5$$ as shown below: $$x^2-3x=10$$ $$=> x^2-3x-10= 0$$ $$=> (x+2)(x-5) = 0$$ $$=> x = -2$$ or $$x = 5$$ Condition 1) $$x^2-4 = 0$$ $$=> (x-2)(x+2) = 0$$ $$=> x = -2$$ or $$x = 2$$ Only $$x = -2$$ also satisfies the original condition, so we have a unique solution. Thus, condition 1) is sufficient. Condition 2) Since $$x < 6$$ from condition 2) and $$x = -2$$ or $$x = 5$$ from the original condition, $$x = -2$$ or $$x = 5$$. Since we don’t have a unique solution, condition 2) is not sufficient. Therefore, A is the answer. Answer: A 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$149 for 3 month Online Course"
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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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16 Oct 2018, 19:07
Easy approach
If x^2−3x =10 , what is the value of x?

1)x^2−4=0
2)x<6
Statement 1 we get 2 values of x as 2 and -2 out of which only -2 satisfies the equation. So 1 alone is suffice

Now from statement 2 x<6, we can get two values satisfying the equation x=-2 and x=5
Hence Statement 2 alone is not suffice as we are not getting unique value
Answer - Option A
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Re: If x^2-3x=10, what is the value of x?   [#permalink] 16 Oct 2018, 19:07
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# If x^2-3x=10, what is the value of x?

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