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DS problem

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Source: — Data Sufficiency |
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by shankar.ashwin » Fri Jan 27, 2012 7:50 pm
Is |x| < 1 (or) is x between (-1,1) ?

(1) x/|x| is either = 1 (or) = -1

1 < x (or) -1 < x

x could be 2 (or) -1/2 - Insufficient

(2) tells us x is -ve - Insufficient alone

TOgether, x can only take values from (-1 to 0) and |x| < 1 for all values in that range. Sufficient C IMO
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by Anurag@Gurome » Fri Jan 27, 2012 8:04 pm
Mr.Hollywood wrote:Here is a Data Sufficiency problem, anybody knows how to solve?

Is |x| <1?

1) x/|x|<x
2) x<|x|

Thanks guys!
(1) x/|x| < x
If x = 2, then x/|x| = 2/2 = 1, which is less than 2. Here |x| > 1.
If x = -1/2, then x/|x| = (-1/2)/(1/2) = -1, which is less than -1/2. Here |x| < 1.
No definite answer; NOT sufficient.

(2) x < |x|
If x = -2, then |x| = 2 > 1.
If x = -1/2, then |x| = 1/2 < 1.
No definite answer; NOT sufficient.

Combining (1) and (2), |x| will always be < 1 since x will always lie between 0 and -1.

The correct answer is C.
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by hyena1986 » Sat Jan 28, 2012 6:45 am
Can we not rephrase the first equation
as x/|x| < x
=> x/x < |x|
=> 1 < |x|

Sufficient.


Please let me know whats the error in the method?
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by rijul007 » Sat Jan 28, 2012 11:40 am
hyena1986 wrote:Can we not rephrase the first equation
as x/|x| < x
=> x/x < |x|
=> 1 < |x|

Sufficient.


Please let me know whats the error in the method?
hyena1986.. whenever you cross multiply, you need to check whether the number that is being cross multiplied is positive or negative

for eg

-2 < -1
if you cross multiply without checking the signs
you would get 2<1 which is not true

whenever there is a negative involved in cross multiplication, change the inequality signs
-2 < -1
if you multiply both sides by -1
replace "<" by ">"
2>1

In statement 1,
x/|x| < x

if x is positive
1 < x
which implies that |x| > 1

if x is negative
-1 < x
which implies that |x| < 1

INSUFFICIENT
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by Mr.Hollywood » Tue Jan 31, 2012 10:45 pm
Thank you. I was also wondering is there any trick when it comes down to picking smart numbers (ie:if x=2 or x=-1/2)
Anurag@Gurome wrote:
Mr.Hollywood wrote:Here is a Data Sufficiency problem, anybody knows how to solve?

Is |x| <1?

1) x/|x|<x
2) x<|x|

Thanks guys!
(1) x/|x| < x
If x = 2, then x/|x| = 2/2 = 1, which is less than 2. Here |x| > 1.
If x = -1/2, then x/|x| = (-1/2)/(1/2) = -1, which is less than -1/2. Here |x| < 1.
No definite answer; NOT sufficient.

(2) x < |x|
If x = -2, then |x| = 2 > 1.
If x = -1/2, then |x| = 1/2 < 1.
No definite answer; NOT sufficient.

Combining (1) and (2), |x| will always be < 1 since x will always lie between 0 and -1.

The correct answer is C.
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