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If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the

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Bunuel
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If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the [#permalink] If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the   05 Jan 2022, 09:45
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If \(x ≠ 2\), then \((x^2-7x+10)* \frac{x+5}{x-2}\) is equivalent to which of the following?

(A) \(x^2 − 25\)

(B) \(x^2 + 10x + 25\)

(C) \(x + 5\)

(D) \(x^2 +25\)

(E) \(x^2+5\)
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Re: If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the [#permalink] If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the   10 Apr 2022, 07:46
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Bunuel wrote:
If \(x ≠ 2\), then \(x^2-7x+10 \times \frac{x+5}{x-2}\) is equivalent to which of the following?

(A) \(x^2 − 25\)

(B) \(x^2 + 10x + 25\)

(C) \(x + 5\)

(D) \(x^2 +25\)

(E) \(x^2+5\)


STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices for equivalency.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also try to simplify the expression so that it matches one of the answer choices.
I think testing for equivalency will be faster, so I'll go with that...

Key concept: If two expressions are equivalent, they must evaluate to the same value for every possible value of x.
For example, since the expression 2x + 3x is equivalent to the expression 5x, the two expressions will evaluate to the same number for every value of x.
So, if x = 7, the expression 2x + 3x = 2(7) + 3(7) = 14 + 21 = 35, and the expression 5x = 5(7) = 35

Let's test an easy value like \(x = 0\).
Plug \(x = 0\) into the given expression to get: \(0^2-7(0)+10 \times \frac{0+5}{0-2} = 10 \times \frac{5}{-2} = \frac{50}{-2} = -25\)

Now we'll plug \(x = 0\) into the five answer choices see which one(s) evaluate(s) to \(-25\)

(A) \(0^2 − 25 = -25\). GREAT! Keep.

(B) \(0^2 + 10(0)x + 25 = 25\). ELIMINATE

(C) \(0 + 5 = 5\). ELIMINATE

(D) \(0^2 +25 = 25\). ELIMINATE

(E) \(0^2+5 = 5\). ELIMINATE

Answer: A
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Re: If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the [#permalink] If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the   05 Jan 2022, 09:57
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x^2-7x+10 * x+5/x-2 => [(x-5) * (x-2)] *(x+5)/x-2 => (x-2) cancels => (x-5) * (x+5) => x^2 - 25 (i.e. the difference of squares) => Answer A
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Re: If x 2, then (x^2 - 7x + 10)*(x+5)/x-2 is equivalent to which of the [#permalink]
05 Jan 2022, 09:57
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