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x|x|<2^x?

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x|x|<2^x?

by stoy4o » Sat Feb 04, 2012 11:56 am
If x is an integer, is x|x| < 2^x?

1) x < 0
2) x=-10

OA: D

I chose E. Can someone explain why my reasoning below is incorrect?

1) Insufficient:

Picked x = - 1
-1*|x| < 1/2
|x| > - 1/2
|x| = +/- 1
a. |x| = -1 => -1 < -1/2 => 1 > 1/2 => true
b. |x| = 1 => 1 < -1/2 => false

2) Insufficient
a. |x| = 10 => -10*10 = < 2^10 => 100 > 2^10 => true
b. |x| = -10 => 100 < 2^-10 => false
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Source: — Data Sufficiency |
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by santhoshsram » Sat Feb 04, 2012 4:50 pm
If you pick x = -1, then lets look at LHS

LHS is -1*|-1| = -1*(+1) = -1 => Negative

RHS is 2^x. For any x positive or negative or zero, 2^x is always positive

So LHS (negative) < RHS (positive)

Sufficient.

In your explanation,

Picked x = - 1
-1*|x| < 1/2
|x| > - 1/2
|x| = +/- 1 ===>>> This is the issue (I think).

As long you don't know the value of x (+ or -) then |x| = +/-(x). But when you know the value of x, you don't need the +/- anymore, have a deterministic answer for the value of |x|. Whatever x is, |x| is always positive, so if x = -1, then |x| = 1 and not +/-1

Hope that helps.
-- Santhosh S
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by stoy4o » Sat Feb 04, 2012 5:05 pm
I see. Thank you, santhoshsram.
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by neerajkumar1_1 » Sat Feb 04, 2012 11:07 pm
stoy4o wrote:If x is an integer, is x|x| < 2^x?

1) x < 0
2) x=-10

OA: D

I chose E. Can someone explain why my reasoning below is incorrect?

1) Insufficient:

Picked x = - 1
-1*|x| < 1/2
|x| > - 1/2
|x| = +/- 1
a. |x| = -1 => -1 < -1/2 => 1 > 1/2 => true
b. |x| = 1 => 1 < -1/2 => false

2) Insufficient
a. |x| = 10 => -10*10 = < 2^10 => 100 > 2^10 => true
b. |x| = -10 => 100 < 2^-10 => false
try to simplify your every data question...
the equation looks daunting at first.. but what is it really testing u on..

Look at equation closely
x|X|<2^x
now RHS will always be +ve ( for e.g 2^2 = 4 and 2^(-2)=1/4 ...)
Now Lets look LHS.
|x| is always +ve
we are left with x
for the equation to be true x will have to be negative.. so that u can get -ve < +ve

Hence u r checking for whether x is +ve or -ve.

Both statements tell u x is negative.

Hence IMO: D

Hope it helps..
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by neerajkumar1_1 » Sat Feb 04, 2012 11:08 pm
stoy4o wrote:If x is an integer, is x|x| < 2^x?

1) x < 0
2) x=-10

OA: D

I chose E. Can someone explain why my reasoning below is incorrect?

1) Insufficient:

Picked x = - 1
-1*|x| < 1/2
|x| > - 1/2
|x| = +/- 1
a. |x| = -1 => -1 < -1/2 => 1 > 1/2 => true
b. |x| = 1 => 1 < -1/2 => false

2) Insufficient
a. |x| = 10 => -10*10 = < 2^10 => 100 > 2^10 => true
b. |x| = -10 => 100 < 2^-10 => false
try to simplify your every data question...
the equation looks daunting at first.. but what is it really testing u on..

Look at equation closely
x|X|<2^x
now RHS will always be +ve ( for e.g 2^2 = 4 and 2^(-2)=1/4 ...)
Now Lets look LHS.
|x| is always +ve
we are left with x
for the equation to be true x will have to be negative.. so that u can get -ve < +ve

Hence u r checking for whether x is +ve or -ve.

Both statements tell u x is negative.

Hence IMO: D

Hope it helps..
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