Is x > 0 ?
(1) |x + 3| = 4x - 3
(2) |x + 1| = 2x - 1
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Is x > 0?
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gmatdriller
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[email protected]
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ans is ddd
from 1: |x + 3| = 4x - 3
if x > 0, than x+3 = 4x -3 by solving this we get 6= 3x. thus x =2
if x< 0, than x +3 = -4x + 3, by solving this we get x =0 . but if we put x=0 in the question than we see that |x + 3| is not equal to 4x - 3. thus x is not equal to 0
(YOU CAN SEE THAT IF WE PUT X=2 IN THE INEQUALITY WE GET |x + 3| = 4x - 3
HENCE X = 2 THUS X >1
IN THE QUESTIONS RELATED TO MODE ALWAYS CROSS VERIFY THE INEQUALITY BY PUTTING VALUE IN THE QUESTION.
FROM 2: |x + 1| = 2x - 1
IF X>0 THAN, X+1 = 2X-1 . bY SOLVING THIS WE GET X= 2
IF X<0 THAN X+1 =2X-1. BY SOLVING THIS WE GET X = 0
PUT BOTH VALUES IN THE ORIGINAL INEQUALITIES. YOU WILL FIND THAT ONLY X=2 HOLD TRUE. THUS X= 2
HENCE ANSWER SHOULD BE D
from 1: |x + 3| = 4x - 3
if x > 0, than x+3 = 4x -3 by solving this we get 6= 3x. thus x =2
if x< 0, than x +3 = -4x + 3, by solving this we get x =0 . but if we put x=0 in the question than we see that |x + 3| is not equal to 4x - 3. thus x is not equal to 0
(YOU CAN SEE THAT IF WE PUT X=2 IN THE INEQUALITY WE GET |x + 3| = 4x - 3
HENCE X = 2 THUS X >1
IN THE QUESTIONS RELATED TO MODE ALWAYS CROSS VERIFY THE INEQUALITY BY PUTTING VALUE IN THE QUESTION.
FROM 2: |x + 1| = 2x - 1
IF X>0 THAN, X+1 = 2X-1 . bY SOLVING THIS WE GET X= 2
IF X<0 THAN X+1 =2X-1. BY SOLVING THIS WE GET X = 0
PUT BOTH VALUES IN THE ORIGINAL INEQUALITIES. YOU WILL FIND THAT ONLY X=2 HOLD TRUE. THUS X= 2
HENCE ANSWER SHOULD BE D
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gmatdriller
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my concern is, considering the test condition, must we always substitute
to confirm which of the solution is correct? I feel there are other ways
to arrive at the answer without carrying out his check.
For example, we know that the expression in an absolute sign is always >= 0
so, from (1) we can say 4x - 3 >= 0
and x >= 4/3. Also, x > 0. Sufficient
By the same token, x >= 1/2 and thus > 0
Also sufficient.
Can anyone point an error in my explanations please.
to confirm which of the solution is correct? I feel there are other ways
to arrive at the answer without carrying out his check.
For example, we know that the expression in an absolute sign is always >= 0
so, from (1) we can say 4x - 3 >= 0
and x >= 4/3. Also, x > 0. Sufficient
By the same token, x >= 1/2 and thus > 0
Also sufficient.
Can anyone point an error in my explanations please.
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Ian Stewart
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That's the fast way to do the problem, and it's perfectly correct.gmatdriller wrote:
For example, we know that the expression in an absolute sign is always >= 0
so, from (1) we can say 4x - 3 >= 0
and x >= 4/3. Also, x > 0. Sufficient
By the same token, x >= 1/2 and thus > 0
Also sufficient.
Your analysis of these cases isn't quite right. |x+3| is equal to x+3 when *what's inside the absolute value* is positive. So |x+3| = x+3 when x > -3, not when x > 0. You then find, solving, the perfectly good solution x = 2. In the second case, |x+3| = -x-3 when what's inside the absolute value is negative. That is, |x+3| = -x-3 when x < -3 (and not when x < 0; |x+3| is still equal to x+3 if you plug in x = -1, say). So in the second case, when x < -3, we'd find, solving, that x = 0, but this solution doesn't agree with our assumption that x < -3, so cannot be a valid solution. You don't need to plug the value back into the equation.[email protected] wrote:ans is ddd
from 1: |x + 3| = 4x - 3
if x > 0, than x+3 = 4x -3 by solving this we get 6= 3x. thus x =2
if x< 0, than x +3 = -4x + 3, by solving this we get x =0 . but if we put x=0 in the question than we see that |x + 3| is not equal to 4x - 3. thus x is not equal to 0
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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gmatdriller
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I appreciate your explanations, Ian.
First assumption when absolute expression > 0
Is that x>-3; we got x =2....satisfied and x>0. Sufficient
Second assumption absolute expression < 0
Is that x < -3; but we got x= 0..Not a solution.
Not sufficient.
Thanks all for your inputs.
First assumption when absolute expression > 0
Is that x>-3; we got x =2....satisfied and x>0. Sufficient
Second assumption absolute expression < 0
Is that x < -3; but we got x= 0..Not a solution.
Not sufficient.
Thanks all for your inputs.
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gmatdriller
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Have you gone through the previous posts?jaguar123 wrote:I get x = 2,0 in the both the choices. Can any help -
why to choose A in a easy way.
If yes and you still having problems, let me know for further explanations.
