Is x 1 ? (1) |x + 5| = 2x - 4 (2) |x - 4| = |3x - 9|

Question

Is x > 1 ?

(1) |x + 5| = 2x - 4 
(2) |x - 4| = |3x - 9|

Kinshook · Answer

Asked: Is x > 1 ?

(1) |x + 5| = 2x - 4
Case 1: x >= -5
x + 5 = 2x - 4
x = 9
Case 2: x < -5
-x - 5 = 2x -4
3x = -1
x = - 1/3: Not feasible since x < -5
x = 9
SUFFICIENT

(2) |x - 4| = |3x - 9|
Case 1: x < 3
4 - x = 9 - 3x
2x = 5
x = 2.5: Not feasible since x < 3
Case 2: 3=<x<=4
4-x = 3x - 9
4x = 13
x = 13/4 = 3.25
Case 3: x > 4
x - 4 = 3x - 9
2x = 5
x = 2.5; Not feasible since x > 4
x = 3.25
SUFFICIENT

IMO D

AndrewN · Answer

Once again, I find conflicting information between the statements concerning what the unknown can equal. (I say "once again" because  another recent post  by this user, also on absolute value/modulus, was transcribed incorrectly and led to conflicting information.)

The first statement is easier to work with for most people than the second, so that would be a good place to start.

Statement (1): |x + 5| = 2x - 4

Solution 1: x + 5 = 2x - 4 --> x = 9
Solution 2: -(x + 5) = 2x - 4 --> -x - 5 = 2x - 4 --> -1 = 3x --> -1/3 = x

Solution 2 is invalid, because the right-hand side of |x + 5| = 2x - 4 will be negative. Since 9 > 1, the answer to the question is Yes, and  Statement (1) is SUFFICIENT .

Statement (2): |x - 4| = |3x - 9|

Believe it or not, you can treat a double absolute value, in which each side is an expression within an absolute value, the same way you would the earlier equation. To illustrate, solutions 1 and 2 below will solve by manipulating the left-hand side, and 3 and 4 by manipulating the right-hand side.

Solution 1: x - 4 = 3x - 9 --> 5 = 2x --> 2.5 = x
Solution 2: -(x - 4) = 3x - 9 --> -x + 4 = 3x - 9 --> 13 = 4x --> 13/4 = x

Solution 3: x - 4 = 3x - 9 --> 5 = 2x --> 2.5 = x
Solution 4: x - 4 = -(3x - 9) --> x - 4 = -3x + 9 --> 4x = 13 --> x = 13/4

So, it makes no difference whether you choose to work from the right- or left-hand side. In both cases, you drop the absolute value and follow the above steps to arrive at the solutions. Notice that regardless of what  x  actually equals, the value will be greater than 1, so there is no need to test the two solutions.  Statement (2) is SUFFICIENT, and  the answer to the question must be (D)  .

Still, I find it unsatisfying that one statement tells us that x = 5 while the other tells us that  x  equals two other values. As I wrote in my response to the since edited question in that other thread,  the GMAT™ will always provide consistent information about an unknown between the two statements .

Good luck with your studies, everyone.

- Andrew

Shhh103 · Answer

statement 1 is suff

x+5 >0
x = 9

sufficient

statement 2 
we can check for the expresssion
- (x-4)= 3x-9
x = 13/4

or 
x-4 = 3x -9
x = 2.5

both cases x >1
suffcient hence ans is d

rickygo01 · Answer

I solved this DS without doing any particular calculations:

Statement 1: |x + 5| = 2x - 4 given this equation, I know for sure that 2x-4 >/= 0 because we are comparing it with an absolute value which is always >/= 0. If we solve it we obtain that x>2. So X must be > than 1. Sufficient

Statement 2: |x - 4| = |3x - 9| this equation will never be respected for negative values, just take a look at it and you will realize this; as a consequence given that our x cannot be 0 as well, x must be a value greater than 1. Sufficient

So the answer is D

bumpbot · Answer

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Is x > 1 ? (1) |x + 5| = 2x - 4 (2) |x - 4| = |3x - 9|

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