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GMAT - Data Sufficiency - Absolute value - Algebra

If x is an integer, is x|x|<2^x ?

If x is an integer, is x|x|<2x ?

(1) x < 0
(2) x = -10

Statament 1:

x < 0

also we know |x| > 0

since positive x negative = negative

x |x| < 0 ... 1

also,

2x for real x is always positive

i.e. 2x > 0 ...2

from 1 and 1

x |x| < 2x

Sufficient

Statement 2:

x = -10

since x < 0 we can invoke statement 1 and say statement 2 is also sufficient

Statament 1:

x < 0

also we know |x| > 0

since positive x negative = negative

x |x| < 0 ... 1

also,

2x for real x is always positive

i.e. 2x > 0 ...2

from 1 and 1

x |x| < 2x

Sufficient

Statement 2:

x = -10

since x < 0 we can invoke statement 1 and say statement 2 is also sufficient