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# If x^2 - 2x - 15 = 0 and x > 0, which of the following must

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If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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03 Feb 2014, 01:16
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x^2 - 2x - 15 = 0 and x > 0, which of the following must be equal to 0 ?

I. x^2 - 6x + 9
II. x^2 -7x + 10
III. x^2 - 10x + 25

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

Problem Solving
Question: 72
Category: Algebra Second-degree equations
Page: 71
Difficulty: 600

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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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03 Feb 2014, 01:16
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SOLUTION

If x^2 - 2x - 15 = 0 and x > 0, which of the following must be equal to 0 ?

I. x^2 - 6x + 9
II. x^2 -7x + 10
III. x^2 - 10x + 25

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

Factor $$x^2 - 2x - 15 = 0$$ --> $$(x-5)(x+3)=0$$ --> $$x=5$$ or $$x=-3$$. Since given that x>0, then $$x=5$$ only.

Now, substitute $$x=5$$ into the options to see which one equals to 0. Only II and III give 0.

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##### General Discussion
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Joined: 03 Feb 2014
Posts: 7
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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03 Feb 2014, 02:04
1
2
Remember the formula for second degree equations and solve for x(1) x(2):
x(1) + x(2) = - (-2)
x(1)*x(2)= -15

x(1) = -3
X(2)= 5

Now given that x>0, x must be equal to 5.
only II and III include a 5 given the last terms are 10 (II) and 25 (III). Hence, we have to check if they include a positive or negative 5.
=> The solution for II is 2, 5. Sufficient
=> The solution for III is 5, 5. Sufficient

Solution: D
Intern
Joined: 30 Jan 2014
Posts: 17
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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03 Feb 2014, 02:57
1
Can see from the first equation that:
(x-5)*(x+3)=0
And since x>0 than x=5

1) 25-30 = 5
2) 25-35+10 = 0
2) 25-50+25 = 0

so D.
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Joined: 20 Dec 2013
Posts: 221
Location: India
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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03 Feb 2014, 11:23
1
Ans. D

x^2 -2x - 15=0
x^2 - 5x + 3x -15=0
(x+3)(x-5)=0
x=5 (x=-3 is not possible since x>0)

II and III statements have (x-5) as factors therefore will be '0'.
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Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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04 Feb 2014, 01:49
1
Solve x^2 - 2x - 15 = 0:
(x-5)(x+3) = 0;
x = -3, 5.

Since x is given as positive(x > 0), x = 5 is the valid one.

Substitute the value of x = 5 in the equations:
I. 25 - 30 + 9 = 4#0; Reject.
II. 25 - 35 + 10 = 0; Correct.
III. 25 - 50 + 25 = 0; Correct.

II and III only.

Ans is (D).
Intern
Joined: 01 May 2017
Posts: 34
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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07 Jan 2019, 09:50
Factor x2−2x−15=0 --> (x−5)(x+3)=0 --> x=5 or x=−3. Since given that x>0, then x=5 only.

Now, substitute x=5 into the options to see which one equals to 0.

Only II and III give 0.

Intern
Joined: 13 May 2018
Posts: 5
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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01 Dec 2019, 10:22
Can someone help me understand the factoring?

When working through the problem timed, I got

1) x^2-2x-15 = 0
2) (X+3)(X-5)
3) X>0 so x=3

4) 3^2-6^2+9=0 YES
5)3^2-7(3)+10=-2 NO
6)3^2-10(3)+25=4 NO

Why is it unacceptable to not factor the equation as (X+3)(X-5) instead of (X-5)(X+3)?

Any help is appreciated.
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Joined: 06 Aug 2018
Posts: 39
GMAT 1: 600 Q43 V30
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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02 Dec 2019, 06:08
longhorn52 wrote:
Can someone help me understand the factoring?

When working through the problem timed, I got

1) x^2-2x-15 = 0
2) (X+3)(X-5)
3) X>0 so x=3

4) 3^2-6^2+9=0 YES
5)3^2-7(3)+10=-2 NO
6)3^2-10(3)+25=4 NO

Why is it unacceptable to not factor the equation as (X+3)(X-5) instead of (X-5)(X+3)?

Any help is appreciated.

In point no 3 you have made a mistake, the actual value should be x=-3 OR x =5 .
Intern
Joined: 06 Jul 2018
Posts: 8
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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06 Jan 2020, 09:48
x^2-2x-15=0
x^2-5x+3x-15=0
(x+3)(x-5)=0
x=-3 or x=5

as given x>0 => x=5

now substitute in given 3 equations. Only Equations 2 and 3 satisfies the value of x=5
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must   [#permalink] 06 Jan 2020, 09:48
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