Walkabout wrote:
If x is an integer, is x|x|<2^x ?
(1) x < 0
(2) x = -10
Target question: Is x|x|< 2^x ? Given: x is an integer Statement 1: x < 0 In other words, x is NEGATIVE
So, x|x| = (NEGATIVE)(|NEGATIVE|) = (NEGATIVE)(POSITIVE) = NEGATIVE
IMPORTANT: 2^x will be POSITIVE for all values of x.
Since x|x| must be NEGATIVE, and since 2^x must be POSITIVE, we can be
certain that
x|x|< 2^x Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = -10 So, x|x| = (-10)(|-10|) = (-10)(10) = -100 = a NEGATIVE
On the other hand, 2^x = 2^(-10) = 1/(2^10) = some POSITIVE number
Since x|x| is NEGATIVE, and since 2^x must be POSITIVE, we can be
certain that
x|x|< 2^x Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer:
but isn't |x| = -x when x<0 ? based on this logic it should be Negative * Negative = + ive isn't it ??