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

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

by Max@Math Revolution » Mon Oct 08, 2018 12:49 am

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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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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Oct 08, 2018 5:42 am

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Max@Math Revolution 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

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Brent
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by Max@Math Revolution » Tue Oct 09, 2018 11:48 pm

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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.

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.
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