GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 21 Feb 2020, 13:30 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x^2 - 2x - 15 = 0 and x > 0, which of the following must

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61385
If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

3
18 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:28) correct 24% (01:45) wrong based on 1243 sessions

### HideShow timer Statistics

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 61385
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

3
2
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.

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

### Show Tags

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]

### Show Tags

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.
Manager  Joined: 20 Dec 2013
Posts: 220
Location: India
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

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'.
Manager  Status: GMATting
Joined: 21 Mar 2011
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]

### Show Tags

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  B
Joined: 30 Apr 2017
Posts: 34
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

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  B
Joined: 13 May 2018
Posts: 6
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

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.
Intern  B
Joined: 06 Aug 2018
Posts: 48
GMAT 1: 600 Q43 V30 Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

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  B
Joined: 06 Jul 2018
Posts: 8
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must  [#permalink]

### Show Tags

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, 08:48
Display posts from previous: Sort by

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