NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 23:00 It is currently 24 Apr 2024, 23:00
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Difficulty: 505-555 Levelx   Algebrax                     
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618856 [38]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] New post   03 Feb 2014, 01:16
5
Kudos
32
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

80% (01:30) correct 20% (01:49) wrong based on 2970 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618856 [11]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] New post   03 Feb 2014, 01:16
3
Kudos
8
Bookmarks
Expert Reply
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.
General Discussion
avatar
Fabino26
Intern
Intern
Joined: 03 Feb 2014
Posts: 6
Own Kudos [?]: 44 [3]
Given Kudos: 5
Send PM
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] New post   03 Feb 2014, 02:04
1
Kudos
2
Bookmarks
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
avatar
B
AKG1593
Manager
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 290 [1]
Given Kudos: 35
Location: India
Send PM
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] New post   03 Feb 2014, 11:23
1
Kudos
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'.
User avatar
nutshell
Manager
Manager
Joined: 21 Mar 2011
Status:GMATting
Posts: 96
Own Kudos [?]: 279 [2]
Given Kudos: 104
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Send PM
GMAT ToolKit User
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] New post   04 Feb 2014, 01:49
2
Kudos
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).
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6821
Own Kudos [?]: 29918 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must be equal [#permalink] New post   30 Sep 2021, 06:53
1
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
If \(x^2-2x-15=0\) and \(x>0\), which of the following must be equal to zero ?

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


Given: \(x^2-2x-15=0\)
Factor: \((x-5)(x+2)=0\)
So, either \(x = 5\) or \(x = -3\)
Since we're told \(x>0\), we know that it must be the case that \(x = 5\)

Now we can plug \(x = 5\) and to each of the given expressions to see which one(s) evaluate to be zero...

I. \(x^2-6x+9\)
We get: \(5^2-6(5)+9=25-30+9=4\)

II. \(x^2-7x+10\)
We get: \(5^2-7(5)+10=25-35+10=0\)

III. \(x^2-10x+25\)
We get: \(5^2-10(5)+25=25-50+25=0\)

Answer: D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32659
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink] New post   13 Jun 2023, 07:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If x^2 - 2x - 15 = 0 and x > 0, which of the following must [#permalink]
13 Jun 2023, 07:12
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions