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

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If -1 < x < 0, which of the following must be true? [#permalink] New post 23 Oct 2011, 09:49
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (01:43) correct 32% (00:56) wrong based on 88 sessions
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-1-x-0-which-of-the-following-must-be-true-146580.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Jul 2013, 02:39, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: must be true [#permalink] New post 13 Dec 2011, 23:26
+1 E

Remember that every negative number whose exponent is odd has a negative number as a result.
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Re: must be true [#permalink] New post 14 Dec 2011, 02:40
all answers are correct and I'll explain

first we know that X is negative and it's between -1 and 0,

1)x3<x2-correct because x3 is negative(---=-) and x2 is posittive(--=+)
2)x5<1-x x5 is negative and 1 minus negative gives 1+positive so it's correct
3)x4<x2 here u should remember that if number is between 0 and 1, square gives less than actual number...u can check for example 0.5 in square is 0.25 which is less than 0.5..so X4 is less than x2
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Re: must be true [#permalink] New post 26 Jul 2013, 21:51
X belongs to (-1,0)


(1). x^3 < X^2

=> X^3 - X^2 < 0
=> X^2 (X-1) < 0

As X^2 will always be positive or zero. only (X-1) contributes to the negativity of the above inequality.

(X-1) < 0 => X <1 so it must be true for X to be in range (-1,0)

(2). X^5 < 1 -X

=> X(X^4+1) < 1
=> X <1 Must be true (As X^4 +1 wil always be greater than 1)


(3). X^4 < X^2

=>X^2(X^2-1) <0
=> (X+1)(X-1) <0

=> -1<X<1 MUST be true

Hence , (E) !!
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Re: If -1 < x < 0, which of the following must be true? [#permalink] New post 27 Jul 2013, 02:40
Expert's post
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-1-x-0-which-of-the-following-must-be-true-146580.html
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Re: If -1 < x < 0, which of the following must be true? [#permalink] New post 27 Jul 2013, 11:25
LalaB wrote:
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-1-x-0-which-of-the-following-must-be-true-146580.html


Picking -1/2 since it -1 < -1/2 < 0.

-1/2^2 = 1/4
-1/2^3 = -1/8
-1/2^4 = 1/16
-1/2^5 = -1/32

Fractions get smaller every time they are multiplied together. For negative numbers raised to an odd power the result will be negative. Knowing these two things makes the comparisons fairly simple.
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Re: If -1 < x < 0, which of the following must be true?   [#permalink] 27 Jul 2013, 11:25
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