Is the number x positive?
(1) On the number line, 0 is closer to x - 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.
It is a good problem , probably a repeat post...
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Number Line problem
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|x| = the distance between 0 and x.Is the number x positive?
(1) On the number line, 0 is closer to x - 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.
|x-y| = the distance between 0 and x-y.
|x+y| = the distance between 0 and x+y.
Statement 1: On the number line, 0 is closer to x - 1 than to x.
|x-1| < |x|.
Since there is absolute value notation on each side, we can square the inequality.
(x-1)² < x²
x² - 2x + 1 < x²
-2x < -1
x > 1/2.
Thus, x must be positive.
SUFFICIENT.
Statement 2: On the number line, 0 is closer to x than to x + 1.
|x| < |x+1|.
Since there is absolute value notation on each side, we can square the inequality.
x² < (x+1)²
x² < x² + 2x + 1
-2x < 1
x > -1/2.
Thus, x could be negative or positive.
INSUFFICIENT.
The correct answer is A.
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Java_85
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IMO A is the answer.
(1) x>0.5 this statement is valid --> x is positive --> YES --> A or D
(2) this statement is valid for x=-0.2 or x=0.2 --> x could be negative --> We don't know if x is positive or negative --> A
(1) x>0.5 this statement is valid --> x is positive --> YES --> A or D
(2) this statement is valid for x=-0.2 or x=0.2 --> x could be negative --> We don't know if x is positive or negative --> A
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Hi mgm,
For this DS question, you'll find it pretty easy to TEST values:
We're asked if x is positive? This is a YES/NO question. We don't know anything about x to start.
For this question you'll find that drawing a picture might be helpful; Number Properties will also make this question a bit easier to handle. Remember what the question's asking for though: Is x positive?
If x > 0 then the answer is YES
If x = 0 then the answer is NO
If x < 0 then the answer is NO
Fact 1 tells us that 0 is closer to (x - 1) than to x.
Here, consider the possibilities...
Could x = 0??? Is 0 closer to -1 than to 0?
No, it's not, so x CANNOT = 0
Could x = a negative?
Try x = -1
Is 0 closer to -2 than to -1
No, it's not, so x CANNOT = a negative
If x CANNOT = 0 and x CANNOT = a negative, then all that's left are positives!!!!
So x MUST be positive and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
Fact 2 tells us that 0 is closer to x than to (x+1)
Let's consider the possibilities here:
Could x = 0???
0 is closer to 0 than to 1, so 0 IS POSSIBLE and the answer to the question is NO.
Could x = 1???
0 is closer to 1 than to 2, so 1 IS POSSIBLE and the answer to the question is YES.
These results are inconsistent.
Fact 2 is INSUFFICIENT
Final Answer:
A
GMAT assassins aren't born, they're made,
Rich
For this DS question, you'll find it pretty easy to TEST values:
We're asked if x is positive? This is a YES/NO question. We don't know anything about x to start.
For this question you'll find that drawing a picture might be helpful; Number Properties will also make this question a bit easier to handle. Remember what the question's asking for though: Is x positive?
If x > 0 then the answer is YES
If x = 0 then the answer is NO
If x < 0 then the answer is NO
Fact 1 tells us that 0 is closer to (x - 1) than to x.
Here, consider the possibilities...
Could x = 0??? Is 0 closer to -1 than to 0?
No, it's not, so x CANNOT = 0
Could x = a negative?
Try x = -1
Is 0 closer to -2 than to -1
No, it's not, so x CANNOT = a negative
If x CANNOT = 0 and x CANNOT = a negative, then all that's left are positives!!!!
So x MUST be positive and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
Fact 2 tells us that 0 is closer to x than to (x+1)
Let's consider the possibilities here:
Could x = 0???
0 is closer to 0 than to 1, so 0 IS POSSIBLE and the answer to the question is NO.
Could x = 1???
0 is closer to 1 than to 2, so 1 IS POSSIBLE and the answer to the question is YES.
These results are inconsistent.
Fact 2 is INSUFFICIENT
Final Answer:
A
GMAT assassins aren't born, they're made,
Rich
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Another approach is the sketch the cases on a number line.mgm wrote:Is the number x positive?
(1) On the number line, 0 is closer to x - 1 than to x.
(2) On the number line, 0 is closer to x than to x + 1.
Target question: Is x positive?
Statement 1: On the number line, 0 is closer to x - 1 than to x.
First, recognize that x-1 will always be to the left of x.
Second, recognize that there are 3 possible ways to place x-1 and x with relation to zero.
If zero is closer to x-1 than to x, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x must be positive
If case #3 is true, we can see that x must be positive
Since both possible cases yield the same answer to the target question, we can answer the target question with certainty.
So, statement 1 is SUFFICIENT
Statement 2: On the number line, 0 is closer to x than to x + 1.
Recognize that x+1 will always be to the right of x.
Also recognize that there are 3 possible ways to place x and x+1 with relation to zero.
If zero is closer to x than to x+1, then we can rule out case #2, leaving us with cases #1 and #3 as possible scenarios.
If case #1 is true, we can see that x is negative
If case #3 is true, we can see that x is positive
Since the two possible cases yield different answers to the target question, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
