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# If -1 < a < 0, q = a - 1, r = a^2, and s = a^3, then which of the foll

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
If -1 < a < 0, q = a - 1, r = a^2, and s = a^3, then which of the foll  [#permalink]

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28 Oct 2018, 22:43
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Difficulty:

45% (medium)

Question Stats:

69% (01:08) correct 31% (01:09) wrong based on 96 sessions

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If $$-1 < a < 0$$, $$q = a - 1$$, $$r = a^2$$, and $$s = a^3$$, then which of the following is true?

A. $$q < r < s$$

B. $$q < s < r$$

C. $$r < q < s$$

D. $$s < q < r$$

E. $$s < r < q$$

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Joined: 18 Jul 2018
Posts: 380
Location: India
Concentration: Finance, Marketing
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Re: If -1 < a < 0, q = a - 1, r = a^2, and s = a^3, then which of the foll  [#permalink]

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29 Oct 2018, 00:07
1
From the question a is negative.

Then q will also be negative.
r will be positive.
and s will be negative.
Since s is cube of a then s will be lesser than q.

$$s<q<r$$

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Manager
Joined: 28 Jun 2018
Posts: 52
Re: If -1 < a < 0, q = a - 1, r = a^2, and s = a^3, then which of the foll  [#permalink]

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29 Oct 2018, 06:28
Taking a= -0.5
Then Q= - 1.5
R = 0.25
S= -0.125

Q< A < S < R

B, methinks.
Director
Joined: 31 Oct 2013
Posts: 797
Concentration: Accounting, Finance
GPA: 3.68
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Re: If -1 < a < 0, q = a - 1, r = a^2, and s = a^3, then which of the foll  [#permalink]

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13 Nov 2018, 15:48
Bunuel wrote:
If $$-1 < a < 0$$, $$q = a - 1$$, $$r = a^2$$, and $$s = a^3$$, then which of the following is true?

A. $$q < r < s$$

B. $$q < s < r$$

C. $$r < q < s$$

D. $$s < q < r$$

E. $$s < r < q$$

a is a negative fraction.

$$a^2 > a^3.$$

q = a -1. As a is negative q must be negative.

2 negative we have . but a^3 yields much smaller than q.

Thus , $$a^2>a^3>q.$$
Re: If -1 < a < 0, q = a - 1, r = a^2, and s = a^3, then which of the foll &nbs [#permalink] 13 Nov 2018, 15:48
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