If -1

Question

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

Bunuel · Accepted Answer

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 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.

HarveyS · Answer

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.

Bunuel · Answer

Consider this:  x^4 < x^2  holds true if  -1<x<0  or  0<x<1 .

Therefore, since given that  -1<x<0 , then  x^4 < x^2  must be true.

Hope it's clear.

ENGRTOMBA2018 · Answer

Make sure to format the question properly. When you select the tag "source-others please specify" , do mention at the end of the question. As for the question look below. You are told that -1 x is a negative fraction less -1. Let us analyse the 3 options. I. x^3 < x^2 ----> MUST BE TRUE as x^2 of 'x' in this question >0 while x^3 <0 . Consider x=-0.5 , x^2=0.25 >0 while x^3=-0.125 <0 . II. x^5 < 1 – x ----> MUST BE TRUE. Odd power of a negative umber x (= x^5 )<0 while 1-x for a negative x >0. Consider x=-0.5 ---> 1-(-0.5)=1+0.5=1.5 >0 III. x^4 < x^2 -----> MUST BE TRUE. For fractions -1x>1, greater the power, smaller will be the number. Consider x=-0.5 , x^2=0.25 , x^4 = 0.0625 , thus x^4 E is the correct answer. Hope this helps.

chetan2u · Answer

Hi, this Qs tests the properties of numbers/ fractions between 0 and 1.. so lets first check the properties, the answer will come automatically.. 1) any even power will always be greater than any odd power.. x^even>x or x^odd.. 2) within even powers-- as we keep increasing power the value will keep becoming lesser.. x^4x 4) Roots-- even roots will be imaginary.. \sqrt{x} not real Odd roots are possible and will be lesser for lower 3rd root will be more than 5th root of x.. or 3rd root of x

TheUltimateWinner · Answer

I. x^3 < x^2 ---> x<1 ---> for negative value of x is less than 1. So, true. II. x^5 < 1 – x ---> x^5+x<1 ---> negative result-negative result<1 ---> negative result<1 ---> So, true. III. x^4 < x^2 ---> x^2<1 ---> for any value of x (according to question stem) it must be less than 1 ---> So, true. So, the correct choice is E to me.

ydmuley · Answer

Try by substituting a value in the equation.

Take x = -1/2 and cross check each option.

I. x^3 < x^2 -   True  
II. x^5 < 1 – x -   True  
III. x^4 < x^2  -   True

Hence, answer is E - All - I, II & III

JeffTargetTestPrep · Answer

We can see that x is a negative number between 0 and -1. Thus, x^odd = negative and x^even = positive. So, I is true.

Furthermore, 1 - x = 1 + |x|, which is positive, so it’s greater than x^5, which is negative. So, II is also true.

Lastly, when x is raised to an even integer power, the larger the even integer, the smaller the power. For example, if x = -1/2, then x^4 = 1/16 and x^2 = 1/4. Thus, x^4 < x^2. So, III is also true .

Answer: E

arvind910619 · Answer

imo E 
take a value of -0.2 then substitute in every equation .
hence all satisfy

shashankism · Answer

Here it is given that -1<x<0 so x is a -ve number greater than -1.
I. x^3 < x^2 is true . X^2 is positive, x^3 is -ve
II. x^5 < 1-x i true. X^5 is -ve , 1-x is +ve.
III. X^4 < x^2 is true. X^4 and x^2 are both +ve. Also since x has a domain (-1,0), x^4 < x^2.

Answer E.

MathRevolution · Answer

-1 < x < 0 which means that 'x' is negative and it is a fraction value or decimal value.

Condition I.  x^3  <  x^2  -  a cube of a negative number is always negative whereas the square of a negative number is always positive.  - This condition is TRUE.

Condition II.  x^5  < 1 – x  - Odd power of a negative number will result in a negative number whereas 1- (negative number) will result in a positive number.   -This condition is TRUE .

Condition III.  x^4  <  x^2   - 4 ^{th}  power of an integer is greater than the square of the same integer. But, here 'x' is a fraction. So denominator of 4 ^{th}  power will be more than denominator of squared power which will result in 4 ^{th}  power of x less than squared of x. (In other words, decimal values gets smaller when raised to higher powers)  - This condition is TRUE.

Answer E.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards