If x is not equal to 0, is |x| less than 1?
(1)x/|x| < x
(2) |x| > x
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Deepthi Subbu
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shankar.ashwin
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C IMO.
Lets looks at the easier statement first.
(2) |x| > x
Implies x is negative (|x| could be less than or greater than 1- Insufficient)
(1) x/|x| can either be 1 or -1 ( 1 = when x is positive, -1 when x is negative)
So, 1<x (or) -1<x(<0) Between 0 and -1 because x should be -ve in this case) 2 cases, Insufficient
Together we know x can only take values from 0 to -1. Hence |x| < 1.
Lets looks at the easier statement first.
(2) |x| > x
Implies x is negative (|x| could be less than or greater than 1- Insufficient)
(1) x/|x| can either be 1 or -1 ( 1 = when x is positive, -1 when x is negative)
So, 1<x (or) -1<x(<0) Between 0 and -1 because x should be -ve in this case) 2 cases, Insufficient
Together we know x can only take values from 0 to -1. Hence |x| < 1.
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sl750
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Prompt can be rephrased as Is -1<x<1 ?
Statement 1
x/|x| < x
|x| can have two solutions depending on whether x is positive on negative
When x is positive ; x>1
When x is negative ; x>-1 . Insufficient
Statement 2
|x|>x
When x is positive; x>x; This can't be true
When x is negative; x<0. Insufficient
Combining statement 1 and 2
From 1, we have x>1 or x>-1
From 2, we have x<0. Therefore only one solution fits,i.e, -1<x<0. This solution is a subset of -1<x<1. Sufficient
Statement 1
x/|x| < x
|x| can have two solutions depending on whether x is positive on negative
When x is positive ; x>1
When x is negative ; x>-1 . Insufficient
Statement 2
|x|>x
When x is positive; x>x; This can't be true
When x is negative; x<0. Insufficient
Combining statement 1 and 2
From 1, we have x>1 or x>-1
From 2, we have x<0. Therefore only one solution fits,i.e, -1<x<0. This solution is a subset of -1<x<1. Sufficient
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GMATGuruNY
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Question rephrased: Is x a positive or negative fraction?Deepthi Subbu wrote:If x is not equal to 0, is |x| less than 1?
(1)x/|x| < x
(2) |x| > x
Plug in the following:
One positive fraction
One positive integer greater than 1
One negative fraction
One negative integer less than -1.
Statement 1: x/|x| < x.
x = 1/2 does not work.
x = 2 works.
x = -1/2 works.
x = -2 does not work.
Since x = -1/2 is between -1 and 1 and x=2 is not, INSUFFICIENT.
Statement 2: |x| > x
x = 1/2 does not work.
x = 2 does not work.
x = -1/2 works.
x = -2 works.
Since x = -1/2 is between -1 and 1 and x=-2 is not, INSUFFICIENT.
Statements 1 and 2 combined:
Only x = -1/2 satisfies both statements.
It is not possible in statement 1 that x=1 or that x=-1.
Thus, we know that x must be a negative fraction.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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maisatomai
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I plugged in -2, -0.5, 0.5, 2 into the 2.
And for
-2: N for 1 and Y for 2
-0.5: Y for 1 for Y for 2
0.5: N for 1 and N for 2
2: Y for 1 and N for 2.
Since more than 1 shows unique pattern (Y for 1 and N for 2), can I conclude it is C because of this?
And for
-2: N for 1 and Y for 2
-0.5: Y for 1 for Y for 2
0.5: N for 1 and N for 2
2: Y for 1 and N for 2.
Since more than 1 shows unique pattern (Y for 1 and N for 2), can I conclude it is C because of this?
