What is x?
(1) |x| < 2
(2) |x| = 3x - 2
[spoiler]OA=B[/spoiler].
How should I solve this DS question? How can I get the value of x from statement (2)?
What is x?
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
- GMATGuruNY
- 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
Statement 1:Gmat_mission wrote:What is x?
(1) |x| < 2
(2) |x| = 3x - 2
Here, x can be any value between -2 and 2.
INSUFFICIENT.
Statement 2:
Case 1: signs unchanged
x = 3x - 2
2 = 2x
1 = x
x = 1.
Case 2: signs changed in the absolute value
-x = 3x - 2
2 = 4x
2/4 = x
x = 1/2.
When an equation has absolute value only ON ONE SIDE, plug the two solutions back into the original equation to ensure that both are valid.
If we plug x=1 into |x| = 3x-2, we get:
|1| = 3*1 - 2
1 = 1.
This works.
x=1 is a valid solution for |x| = 3x-2.
If we plug x=1/2 into |x| = 3x-2, we get:
|1/2| = 3(1/2) - 2
1/2 = -1/2.
Doesn't work.
x=1/2 is NOT a valid solution for |x| = 3x-2.
Thus, Statement 2 has only one valid solution:
x=1.
SUFFICIENT.
The correct answer is B.
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
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
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Hello.
(1) |x|<2.
this implies that x can be 0, 1, 1.5, -10, . . . . . NOT Sufficient.
(2) |x|=3x-2.
Using the definition of absolute value we get two cases: $$(a)\ \ x=3x-2\ \Leftrightarrow\ 2=2x\ \Leftrightarrow\ x=1.$$ $$(b)\ \ -x=3x-2\ \Leftrightarrow\ 2=4x\ \Leftrightarrow\ x=\frac{1}{2}.$$ Now, let's plug the solutions in the original equation: $$\left|1\right|=3\left(1\right)-2\ \Leftrightarrow\ \ 1=3-2\ \Leftrightarrow\ 1=1.$$ $$\left|\frac{1}{2}\right|=3\left(\frac{1}{2}\right)-2\ \Leftrightarrow\ \ \frac{1}{2}=\frac{3}{2}-2\ \Leftrightarrow\ \frac{1}{2}\ne-\frac{1}{2}.$$ Hence, x=1/2 is not a solution.
Therefore, we get one unique solution x=1. Thus, this statement is SUFFICIENT.
The correct answer is the option B.
(1) |x|<2.
this implies that x can be 0, 1, 1.5, -10, . . . . . NOT Sufficient.
(2) |x|=3x-2.
Using the definition of absolute value we get two cases: $$(a)\ \ x=3x-2\ \Leftrightarrow\ 2=2x\ \Leftrightarrow\ x=1.$$ $$(b)\ \ -x=3x-2\ \Leftrightarrow\ 2=4x\ \Leftrightarrow\ x=\frac{1}{2}.$$ Now, let's plug the solutions in the original equation: $$\left|1\right|=3\left(1\right)-2\ \Leftrightarrow\ \ 1=3-2\ \Leftrightarrow\ 1=1.$$ $$\left|\frac{1}{2}\right|=3\left(\frac{1}{2}\right)-2\ \Leftrightarrow\ \ \frac{1}{2}=\frac{3}{2}-2\ \Leftrightarrow\ \frac{1}{2}\ne-\frac{1}{2}.$$ Hence, x=1/2 is not a solution.
Therefore, we get one unique solution x=1. Thus, this statement is SUFFICIENT.
The correct answer is the option B.
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Statement One Alone:Gmat_mission wrote:What is x?
(1) |x| < 2
(2) |x| = 3x - 2
|x| < 2
We see that x < 2 or:
-x < 2
x > -2
So, -2 < x < 2.
Statement one alone is not sufficient to answer the question.
Statement Two Alone:
|x| = 3x - 2
When x is positive we have:
x = 3x - 2
-2x = -2
x = 1
When x is negative we have:
-x = 3x - 2
2 = 4x
1/2 = x
We see that x = 1 matches our assumption that x is positive whereas x = ½ does not match our assumption that x is negative (because x = ½, which is a positive value). Thus, x can be only 1.
Answer: B
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews