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If (x−2.5)(x+0.5)=4, what is the value of x?

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If (x−2.5)(x+0.5)=4, what is the value of x? [#permalink]

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New post 21 Sep 2016, 02:59
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  85% (hard)

Question Stats:

49% (01:44) correct 51% (01:44) wrong based on 111 sessions

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If (x−2.5)(x+0.5)=4, what is the value of x? [#permalink]

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New post 21 Sep 2016, 06:20
(x−2.5)(x+0.5)=4

==> \((x−\frac{5}{2})(x+\frac{1}{2})=4\)
==> \(x^2+\frac{x}{2} - \frac{5x}{2}-\frac{5}{4}=4\)
==> \(x^2- 2x-\frac{21}{4}=0\) (Subtract each side by 4) --Eq1
==> \(x^2 - \frac{7}{2}x + \frac{3}{2}x-\frac{21}{4}=0\)
==> \(x(x - \frac{7}{2}) + \frac{3}{2}(x-\frac{7}{2})=0\)
==> \((x - \frac{7}{2}) (x+ \frac{3}{2})=0\)
==> x = 7/2 or x = - 3/2

(1) (x+1.5)(x−1.5)=0 ==> \(x^2-{1.5}^2\) = 0 ==> x = 1.5 or x = -1.5 -- Sufficient.

(2) (x−3.5)(x+1.5)=0 ==> \(x^2 + \frac{3}{2}x - \frac{7}{2} - \frac{3}{2}*\frac{7}{2}=0\) ==> \(x^2- 2x-\frac{21}{4}=0\) --Same as equation 1. --Not suffici

Ans A .
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Last edited by 0ld on 21 Sep 2016, 06:37, edited 1 time in total.

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Re: If (x−2.5)(x+0.5)=4, what is the value of x? [#permalink]

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Bunuel wrote:
If (x−2.5)(x+0.5) = 4, what is the value of x?

(1) (x+1.5)(x−1.5) = 0

(2) (x − 3.5)(x+1.5) = 0


Target question: What is the value of x?

Given: (x−2.5)(x+0.5) = 4
This information is HUGE, since it tells us the only 2 possible values of x
Given: (x−2.5)(x+0.5) = 4
Expand and simplify to get: x² - 2x - 1.25 = 4
Subtract 4 from both sides: x² - 2x - 5.25 = 0
Multiply both sides by 4 to get: 4x² - 8x - 21 = 0
Factor to get: (2x + 3)(2x - 7) = 0
If 2x + 3 = 0, then x = -3/2 = -1.5
If 2x - 7 = 0, then x = 7/2 = 3.5
So, EITHER x = -1.5 OR x = 3.5
So, which value is it?

Statement 1: (x+1.5)(x−1.5) = 0
This tells us that EITHER x = -1.5 OR x = 1.5
Since we already know that EITHER x = -1.5 OR x = 3.5, we can be certain that x = -1.5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (x − 3.5)(x+1.5) = 0
This tells us that EITHER x = -1.5 OR x = 3.5
Since we already knew that EITHER x = -1.5 OR x = 3.5, this statement provides no new information.
So, all we can conclude from this is that EITHER x = -1.5 OR x = 3.5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:
[Reveal] Spoiler:
A


Cheers,
Brent
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Re: If (x−2.5)(x+0.5)=4, what is the value of x? [#permalink]

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Bunuel wrote:
If (x−2.5)(x+0.5)=4, what is the value of x?

(1) (x+1.5)(x−1.5)=0

(2) (x−3.5)(x+1.5)=0


Looking at this one, it seems like the statements will be much easier to simplify than the question will. I don't really want to go through the process of multiplying out and then re-factoring the quadratic from the question, so I'm just going to start with the statements and see how far I can get.

Statement 1: This says that x is -1.5, or x is 1.5. But it's possible that only one of those fits the constraint from the problem, in which case this statement would actually be sufficient. I'll plug them both in:

(-1.5 - 2.5)(-1.5 + 0.5) = (-4)(-1) = 4. So, x = -1.5 fits the constraint.
(1.5 - 2.5)(1.5 + 0.5) = (-1)(2) = -2. So, x = 1.5 doesn't fit the constraint. The only valid case, which fits both the constraint from the question and Statement 1, is x = -1.5.

So, statement 1 is sufficient.

Statement 2
: Same process. x = 3.5, or x = -1.5. We already know that -1.5 fits the constraint. Does 3.5 fit?

(3.5 - 2.5)(3.5 + 0.5) = (1)(4) = 4.

Unfortunately, both possible values of x are valid. Since this statement gives us two valid values for x, it's insufficient.

The answer is (A).
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Re: If (x−2.5)(x+0.5)=4, what is the value of x? [#permalink]

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New post 24 Feb 2017, 01:12
Prompt analysis
(x -2.5)(x +0.5) = 4 => x^2 -2x -1.25 -4 = 0 =>x^2 -2x -5.25 = 0 => x= 3.5, -1.5

Superset
The answer will either 3.5 or -1.5

Translation
In order to find the value of x, we need
1# exact value of x
2# any other equation which satisfy one of the value of x

Statement analysis
St 1: x = -1.5,1.5. Combining the solution for both the equation we get x = -1.5. ANSWER
St 2: x= 3.5, -1.5. Combining both the equations we get x =x= 3.5, -1.5. INSUFFICIENT as we cannot narrow it down to one.

Option A

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Re: If (x−2.5)(x+0.5)=4, what is the value of x? [#permalink]

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New post 04 Jan 2018, 03:16
the calculation yields a beautiful results. Also, no complex steps are present in this problem. Yes, gmat likes such kind of math problem.

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Re: If (x−2.5)(x+0.5)=4, what is the value of x?   [#permalink] 04 Jan 2018, 03:16
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If (x−2.5)(x+0.5)=4, what is the value of x?

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