What is the value of X ?
1) |X| < 2
2) |X| = 3X-2
OA B
I feel OA is wrong could you please advice me what would be OA ?
Regards,
Uva
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Absolute Values
This topic has expert replies
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: What is the value of x?Uva@90 wrote:What is the value of x ?
1) |x| < 2
2) |x| = 3x - 2
Statement 1: |x| < 2
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1 (notice that < 2)
Case b: x = 0 (notice that |0| < 2)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |x| = 3x - 2
When solving equation involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots
So, first we get:
x = 3x - 2
Solve, to get x = 1
To check whether this is an extraneous, plug x = 1 into the original equation to get: |1| = 3(1) - 2
Simplify to get: |1| = 1
PERFECT, this solution checks out.
Next, we get:
x = -(3x - 2)
Solve, to get x = 1/2
To check whether this is an extraneous, plug x = 1/2 into the original equation to get: |1/2| = 3(1/2) - 2
Simplify to get: |1/2| = -1/2
This solution DOES NOT check out.
So, it MUST be the case that x = 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
Statement 2 is sufficient alone. There are two ways to see that - we have
3x - 2 = |x|
3x = |x| + 2
Notice now that |x| + 2 must be a positive number (since we're adding 2 to something which is zero or greater), so 3x is equal to a positive number, which means x must be positive. If x is positive, then |x| = x, so the equation becomes
3x = x + 2
2x = 2
x = 1
So Statement 2 is sufficient.
I think many test takers will instead use a 'cases' approach, which will also work, as long as you are careful about what you're doing. We start with the equation:
|x| = 3x - 2
If x > 0, then |x| = x, so we get the equation we solved above, and x = 1.
If x < 0, then |x| = -x, and we have
-x = 3x - 2
4x = 2
x = 1/2
But we began by assuming that x was negative, and found that x = 1/2, which is not negative. Our solution contradicts our assumption - it is not a legitimate solution. You can confirm that if you like by plugging it back into the original equation; you'll find it doesn't work.
Since Statement 1 is not sufficient alone, the answer is B.
3x - 2 = |x|
3x = |x| + 2
Notice now that |x| + 2 must be a positive number (since we're adding 2 to something which is zero or greater), so 3x is equal to a positive number, which means x must be positive. If x is positive, then |x| = x, so the equation becomes
3x = x + 2
2x = 2
x = 1
So Statement 2 is sufficient.
I think many test takers will instead use a 'cases' approach, which will also work, as long as you are careful about what you're doing. We start with the equation:
|x| = 3x - 2
If x > 0, then |x| = x, so we get the equation we solved above, and x = 1.
If x < 0, then |x| = -x, and we have
-x = 3x - 2
4x = 2
x = 1/2
But we began by assuming that x was negative, and found that x = 1/2, which is not negative. Our solution contradicts our assumption - it is not a legitimate solution. You can confirm that if you like by plugging it back into the original equation; you'll find it doesn't work.
Since Statement 1 is not sufficient alone, the answer is B.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
-
Uva@90
- Master | Next Rank: 500 Posts
- Posts: 490
- Joined: Thu Jul 04, 2013 7:30 am
- Location: Chennai, India
- Thanked: 83 times
- Followed by:5 members
Thanks Brent,Brent@GMATPrepNow wrote:Target question: What is the value of x?Uva@90 wrote:What is the value of x ?
1) |x| < 2
2) |x| = 3x - 2
Statement 1: |x| < 2
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1 (notice that < 2)
Case b: x = 0 (notice that |0| < 2)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: |x| = 3x - 2
When solving equation involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots
So, first we get:
x = 3x - 2
Solve, to get x = 1
To check whether this is an extraneous, plug x = 1 into the original equation to get: |1| = 3(1) - 2
Simplify to get: |1| = 1
PERFECT, this solution checks out.
Next, we get:
x = -(3x - 2)
Solve, to get x = 1/2
To check whether this is an extraneous, plug x = 1/2 into the original equation to get: |1/2| = 3(1/2) - 2
Simplify to get: |1/2| = -1/2
This solution DOES NOT check out.
So, it MUST be the case that x = 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
I missed the third step of the three steps, hence ended in two solution.
When solving equation involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug in the solutions to check for extraneous roots
Thanks again.
Regards,
Uva.
Known is a drop Unknown is an Ocean
