GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Aug 2018, 10:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Which of the following options correctly describes the relationship be

Author Message
TAGS:

### Hide Tags

Intern
Joined: 21 Apr 2015
Posts: 5
Which of the following options correctly describes the relationship be  [#permalink]

### Show Tags

Updated on: 18 Oct 2017, 03:57
00:00

Difficulty:

25% (medium)

Question Stats:

60% (00:51) correct 40% (00:37) wrong based on 63 sessions

### HideShow timer Statistics

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

Originally posted by vinhthi on 18 Oct 2017, 03:02.
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.
SC Moderator
Joined: 22 May 2016
Posts: 1910
Which of the following options correctly describes the relationship be  [#permalink]

### Show Tags

Updated on: 18 Oct 2017, 04:08
2
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.)

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

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

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

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

$$a < c < d < b$$

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Originally posted by generis on 18 Oct 2017, 04:05.
Last edited by generis on 18 Oct 2017, 04:08, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 48033
Re: Which of the following options correctly describes the relationship be  [#permalink]

### Show Tags

18 Oct 2017, 04:06
2
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
_________________
SC Moderator
Joined: 22 May 2016
Posts: 1910
Which of the following options correctly describes the relationship be  [#permalink]

### Show Tags

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
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3176
Location: United States (CA)
Re: Which of the following options correctly describes the relationship be  [#permalink]

### Show Tags

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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Retired Moderator
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
Re: Which of the following options correctly describes the relationship be  [#permalink]

### Show Tags

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
_________________
Re: Which of the following options correctly describes the relationship be &nbs [#permalink] 22 Oct 2017, 20:02
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.