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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?  [#permalink]

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New post 08 Oct 2018, 01:54
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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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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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New post 08 Oct 2018, 02:07
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!
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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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New post 08 Oct 2018, 02:12
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

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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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New post 08 Oct 2018, 02:13
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

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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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New post 08 Oct 2018, 06:46
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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

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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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New post 10 Oct 2018, 00:56
=>

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.
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Re: If x^2-3x=10, what is the value of x?  [#permalink]

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New post 16 Oct 2018, 20:07
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, 20:07
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