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# Which of the following options correctly describes the relationship be

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Intern
Joined: 21 Apr 2015
Posts: 5

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Which of the following options correctly describes the relationship be [#permalink]

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18 Oct 2017, 03:02
00:00

Difficulty:

35% (medium)

Question Stats:

56% (00:43) correct 44% (00:39) wrong based on 39 sessions

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Given that

a = −0.283
b = a^2
c = a^3
d = a^4

Which of the following options correctly describes the relationship between the 4 numbers?

(A) a < b < c < d
(B) a < c < d < b
(C) c < a < d < b
(D) a < c < b < d
(E) d < c < b < a
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Oct 2017, 03:57, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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VP
Joined: 22 May 2016
Posts: 1108

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Which of the following options correctly describes the relationship be [#permalink]

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18 Oct 2017, 04:05
2
KUDOS
vinhthi wrote:
Hi Guys,

Given that

a=−0.283
b=a2
c=a3
d=a4

Which of the following options correctly describes the relationship between the 4 numbers?

(A) a<b<c<d
(B) a<c< d<b
(C) c<a<d<b
(D) a<c<b<d
(E) d<c<b<a

vinhthi - Yes.

Because the problem is about the behavior of fractions between 0 and -1, it doesn't matter what value you use, as long as it is -1 < x < 0

That decimal is not easy to work with. So I used $$-\frac{1}{2}$$.

(If you like decimals better, you could use -.2, or some other number that is easy to multiply. I find fractions easier with exponential values in this range; I don't have to track on zeros.)

$$a = -\frac{1}{2}$$

$$b = a^2 = -(\frac{1}{2})^2 =\frac{1}{4}$$

$$c = a^3 = -(\frac{1}{2})^3 = -\frac{1}{8}$$

$$d = a^4 = -(\frac{1}{2})^4 = \frac{1}{16}$$

$$a < c < d < b$$

Last edited by genxer123 on 18 Oct 2017, 04:08, edited 2 times in total.

Kudos [?]: 397 [2], given: 640

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135295 [2], given: 12686

Re: Which of the following options correctly describes the relationship be [#permalink]

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18 Oct 2017, 04:06
2
KUDOS
Expert's post
vinhthi wrote:
Given that

a = −0.283
b = a^2
c = a^3
d = a^4

Which of the following options correctly describes the relationship between the 4 numbers?

(A) a < b < c < d
(B) a < c < d < b
(C) c < a < d < b
(D) a < c < b < d
(E) d < c < b < a

Similar question from OG: https://gmatclub.com/forum/if-r-0-345-s ... 32067.html
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Kudos [?]: 135295 [2], given: 12686

VP
Joined: 22 May 2016
Posts: 1108

Kudos [?]: 397 [0], given: 640

Which of the following options correctly describes the relationship be [#permalink]

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18 Oct 2017, 04:42
Bunuel wrote:

Reply posts for this similar and good question contain a mine of information. I had forgotten about it. Thanks, Bunuel

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Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
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Re: Which of the following options correctly describes the relationship be [#permalink]

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22 Oct 2017, 16:52
vinhthi wrote:
Given that

a = −0.283
b = a^2
c = a^3
d = a^4

Which of the following options correctly describes the relationship between the 4 numbers?

(A) a < b < c < d
(B) a < c < d < b
(C) c < a < d < b
(D) a < c < b < d
(E) d < c < b < a

We see that the value of a is negative. Therefore, when it is raised to an odd power, it’s negative, and when it is raised to an even power, it’s positive. Therefore, we see that b and d are positive, and a and c are negative.

Since a is between -1 and 0, when it is raised to an odd power, the larger the exponent, the larger the value. Thus, we have a < a^3 or a < c.

On the other hand, when a is raised to an even power, the larger the exponent, the smaller the value. Thus, we have a^4 < a^2 or d < b.

Thus, the order of the quantities is: a < a^3 < a^4 < a^2, or a < c < d < b.

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Re: Which of the following options correctly describes the relationship be [#permalink]

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22 Oct 2017, 20:02
For convenience, consider a = −0.283 ≈ -.3

Hence,
a = −0.283 = ≈ -0.3
b = a^2 = 0.09
c = a^3 = -0.027
d = a^4 = 0.0081

So we can say, a<c<d<b

Ans: B

Kudos [?]: 190 [0], given: 83

Re: Which of the following options correctly describes the relationship be   [#permalink] 22 Oct 2017, 20:02
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