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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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New post 03 Feb 2014, 01:16
2
15
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:28) correct 23% (01:46) wrong based on 1079 sessions

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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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New post 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.

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

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New post 03 Feb 2014, 02:04
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1
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
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

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

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

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

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New post 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.

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

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

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New post 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 .
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Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must   [#permalink] 02 Dec 2019, 06:08
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