If -1

Question

If  -1 < x < 0 , which of the following must be true?

I.  x < x^2

II.  x^2 < x^3

III.  x < x^3

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

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AdarshSambare · Answer

As x is negative number between -1 and 0:
let x be -1/2 
x = -0.5

I. x<x2
-0.5 < 0.25
Yes for all negative numbers.

II. x2<x3
0.25 < -0.125
No for all negative numbers

III. x<x3
-0.5 < -0.125
Yes for all negative numbers

So, I and III must be true

Option: D

Dereno · Answer

-1 < x < 0 , let’s take x as -(1/2) -1 < -1/2 < 0 , let’s look into the options I. x < x^2 - 1/2 < (-1/2)^2 -1/2 < 1/4 Hence, True. II. x^2 < x^3 (1/4) < -1/8 Hence, False. III. x < x^3 (-1/2) < (-1/2)^3 (-1/2) < (-1/8) multiply by -1, we get 1/2 > 1/8 0.5 > 0.125 Hence, True. Options I and III. Option D

Souradeep17 · Answer

Lets take any number in the range -1/3
Now 
option 1:
1/9>-1/3 (since x^2 will always be positive hence we can say that it will always be more than x hence option 1 is correct.)

option 2:
Now x^3 >x^2 this will never be true as x^3 will always be negative and x^2 will be positive.

Option 3:
here both x^3 and x Will be negative but since x is a negative decimal number the absolute value of x^3 will be always less than x but since both are negative we can say that x^3 will be greater than x (-1/27>-1/3)

hene 1 & 3 should be corrrect which is option D

Reon · Answer

If -1<x<0 , which of the following must be true?
Let, x= -0.2

I. x<x^2 ; (-0.2)<(0.04) ....True

II. x^2 < x^3 ; (0.04)<(-0.008)....False

III. x<x^3 ; (-0.2)<(-0.008)....True

D (I & III only)

If -1 < x < 0, which of the following must be true?

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