Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Updated on: 20 Sep 2018, 07:58
Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:05.
Last edited by EgmatQuantExpert on 20 Sep 2018, 07:58, edited 5 times in total.
Last edited by EgmatQuantExpert on 20 Sep 2018, 07:58, edited 5 times in total.
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:44) correct
37%
(01:43)
wrong
based on 1223
sessions
History
Date
Time
Result
Not Attempted Yet
Different methods to solve absolute value equations and inequalities- Exercise Question #2
If x is an integer, then how many values of x will satisfy the equation ||x - 10| - 6| = 4?
Options
Previous Question | Next Question
To read the article: Different methods to solve absolute value equations and inequalities
If x is an integer, then how many values of x will satisfy the equation ||x - 10| - 6| = 4?
Options
- a) 0
b) 1
c) 2
d) 3
e) 4
Previous Question | Next Question
To read the article: Different methods to solve absolute value equations and inequalities
My Approach:
Ix-10I will always be positive and in order for ||x-10|-6|=4 to be true |x-10|=2 or |x-10|=10
1.
x-10=2
x=12
2.
-x+10=2
x=8
--> x=12 or x=8
1.
x-10=20
x=20
2.
-x+10=10
x=0
Please correct me if I am wrong!!
Edited! Was wrong first time...
Ix-10I will always be positive and in order for ||x-10|-6|=4 to be true |x-10|=2 or |x-10|=10
|x-10|=2
1.
x-10=2
x=12
2.
-x+10=2
x=8
--> x=12 or x=8
|x-10|=10
1.
x-10=20
x=20
2.
-x+10=10
x=0
Left with four values: 0,8,10,12
So Answer: E
Please correct me if I am wrong!!
Edited! Was wrong first time...
General Discussion
Updated on: 20 Sep 2018, 21:06
Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:10.
Last edited by EgmatQuantExpert on 20 Sep 2018, 21:06, edited 4 times in total.
Last edited by EgmatQuantExpert on 20 Sep 2018, 21:06, edited 4 times in total.
Kudos
Bookmarks
Solution
Given:
- • We are given that x is an integer, and
• We are also given an absolute value equation, ||x - 10| - 6| = 4
To find:
- • We need to find the number of values of x, that satisfy the given equation
Approach and Working:
- • As seen in the previous question, the first step is to substitute |x - 10| as t, which gives
- o |t - 6| = 4
- o t - 6 = 4, if t ≥ 6
- Implies, t = 10, which is greater than 6
Now, substituting back t as |x - 10|, we get, |x - 10| = 10
This again gives two cases,
Case -1: x – 10 = 10, if x ≥ 10
Implies, x = 20, which is greater than 10
Thus, x = 20, is a possible value of x
Case -2: x – 10 = -10, if x < 10
Implies, x = 0, which is also a possible value
- Implies, t = 2, which is less than 6
Now, substituting back t as |x - 10|, we get, |x - 10| = 2
This again gives two cases,
Case -1: x – 10 = 2, if x ≥ 10
Implies, x = 12, which is greater than 10
Thus, x = 12, is a possible value of x
Case -2: x – 10 = -2, if x < 10
Implies, x = 8, which is less than 10
Thus, x = 8, is also a possible value
• Therefore, the number of possible values of x is 4.
Hence, the correct answer is option E.
Answer: E
