Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

How many solutions has the equation ||x-3|-2|=1?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

How many solutions has the equation ||x-3|-2|=1?

by Max@Math Revolution » Mon Jan 22, 2018 12:01 am
[GMAT math practice question]

How many solutions has the equation ||x-3|-2|=1?

A. 0
B. 1
C. 2
D. 3
E. 4
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Jan 22, 2018 4:09 am
Max@Math Revolution wrote:[GMAT math practice question]

How many solutions has the equation ||x-3|-2|=1?

A. 0
B. 1
C. 2
D. 3
E. 4
Case 1: |x-3|-2 = 1
|x-3| = 3
If x-3=3, then x=6.
If x-3=-3, then x=0.

Case 2: |x-3|-2 = -1
|x-3| = 1
If x-3=1, then x=4.
If x-3=-1, then x=2.

The equation has the four solutions in blue: 6, 0, 4 and 2.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue Jan 23, 2018 9:10 am
Max@Math Revolution wrote:[GMAT math practice question]

How many solutions has the equation ||x-3|-2|=1?

A. 0
B. 1
C. 2
D. 3
E. 4
We see that |x-3| - 2 could be 1 or -1 since both |1| and |-1| are equal to 1.

1) If |x - 3| - 2 = 1, then |x - 3| = 3. So x - 3 could be 3 or -3.

i) If x - 3 = 3, then x = 6.
ii) If x - 3 = -3, then x = 0.

2) If |x - 3| - 2 = -1, then |x - 3| = 1. So x - 3 could be 1 or -1.

i) If x - 3 = 1, then x = 4.
ii) If x - 3 = -1, then x = 2.

We see that the equation has 4 solutions.

Answer:E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Wed Jan 24, 2018 12:21 am
=>

||x-3|-2|=1
=> |x-3|-2=±1
=> |x-3|=2±1
=> |x-3|=1 or |x-3|=3
=> x-3=±1 or x-3=±3
=> x=3±1 or x=3±3
=> x=2, x = 4, x = 0 or x = 6

Thus, the equation has four solutions.

Therefore, the answer is E.

Answer: E
Top
Post new topic Post Reply
• Page 1 of 1