Is |x|<1?
1.|X+1|=2|x-1|
2.|x-3| is not equal to 0
Please help me with this DS Questions.
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Statement 1: |x + 1| = 2|x - 1|Is |x| < 1 ?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠0
Case 1: No signs changed
x+1 = 2(x-1)
x+1 = 2x - 2
3 = x.
Case 2: Signs changed in ONE of the absolute values
-(x+1) = 2(x-1)
-x-1 = 2x - 2
-3x = -1
x = 1/3.
Since |x|>1 in Case 1 but |x|<1 in Case 2, INSUFFICIENT.
Statement 2: |x - 3| ≠0
In other words, x≠3.
If x=0, then |x|<1.
If x=10, then |x|>1.
INSUFFICIENT.
Statements combined:
Statement 1 requires that x=3 or x=1/3.
Statement 2 requires that x≠3.
Thus, x=1/3, with the result that |x| < 1.
SUFFICIENT.
The correct answer is C.
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Hi Abhijit K,
This DS question is worded in a very specific way and has a number of interesting Number Properties that you can take advantage of.
We're asked if |X| < 1. This is a YES/NO question.
The wording of this question is interesting in that the types of numbers that would give you a YES answer are "limited" - only positive/negative FRACTIONS or the number 0 would give you a YES; all other possibilities would give you a NO. This gets me thinking that I will have to consider possibilities that are fractions.
Fact 1: |X+1| = 2|X-1|
Since this is an equation that involves absolute values, chances are that there are 2 solutions.
IF.....
X = 3, then the answer to the question is NO.
Remember what I noted about fractions earlier....
IF....
X = 1/3, then the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: |X-3| > 0
This inequality excludes ONLY 1 value of X: 3
X CANNOT be 3....
IF....
X = 4, then the answer to the question is NO.
IF....
X = 1/3, then the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we know....
X is either 3 or 1/3
X CANNOT be 3
This leaves us with just one answer (1/3) and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This DS question is worded in a very specific way and has a number of interesting Number Properties that you can take advantage of.
We're asked if |X| < 1. This is a YES/NO question.
The wording of this question is interesting in that the types of numbers that would give you a YES answer are "limited" - only positive/negative FRACTIONS or the number 0 would give you a YES; all other possibilities would give you a NO. This gets me thinking that I will have to consider possibilities that are fractions.
Fact 1: |X+1| = 2|X-1|
Since this is an equation that involves absolute values, chances are that there are 2 solutions.
IF.....
X = 3, then the answer to the question is NO.
Remember what I noted about fractions earlier....
IF....
X = 1/3, then the answer to the question is YES.
Fact 1 is INSUFFICIENT
Fact 2: |X-3| > 0
This inequality excludes ONLY 1 value of X: 3
X CANNOT be 3....
IF....
X = 4, then the answer to the question is NO.
IF....
X = 1/3, then the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we know....
X is either 3 or 1/3
X CANNOT be 3
This leaves us with just one answer (1/3) and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
