Bunuel wrote:
rakesh20j wrote:
if -1<x<o, which of following must be true?
1) x^3<x^2 2) x^5<1-x 3) x^4<x^2
A. I only B. I and II C. I II and III D. I and III E. II and III
1) x^3<x^2 2) x^5<1-x 3) x^4<x^2
A. I only B. I and II C. I II and III D. I and III E. II and III
The question should read:
If -1 < x < 0, which of the following must be true?
I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III
I. x^3 < x^2 --> from -1 < x < 0 it follows that LHS<0<RHS, so this statement is true.
II. x^5 < 1 – x --> x(x^4+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.
III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 0, then x^2 must be less than 1. Hence, this statement is also true.
Answer: E.
Hope it's clear.
Bunuel,
Did not understand the colored part.
As -1 < x < 0, then X will always be negative and X2 will always be positive, so how to derive that x<1.