It is currently 23 Feb 2018, 06:47

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Aug 2011
Posts: 194
Location: United States
Concentration: Economics, Finance
GMAT Date: 10-16-2013
GPA: 3
WE: Analyst (Computer Software)
A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

18 May 2014, 04:04
3
KUDOS
27
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

37% (00:55) correct 63% (01:02) wrong based on 378 sessions

### HideShow timer Statistics

A set contains the following 5 numbers: $$a^2, a^5, a, \frac{a}{2}, \frac{a}{5}$$. Is the range of the set equal to $$a^2 - a^5$$?

(1) a is negative
(2) $$a^5 < a$$
[Reveal] Spoiler: OA

_________________

Kudos me if you like my post !!!!

Last edited by Nevernevergiveup on 25 Mar 2016, 03:55, edited 3 times in total.
Edited the question and original answer was incorrect.
Intern
Joined: 13 Dec 2013
Posts: 8
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

18 May 2014, 05:13
akhil911 wrote:
A set contains the following 5 numbers: a^2,a^5,a,a/2, and a/5. Is the range of the set equal to a^2–a^5?

1. a is negative
2. a^5<a

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C. Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Kudos me if you like the post !!!!

Hi Akhil

IMO it should be B.

As a^5 is less than a, it means that a is between 0 and 1. Hence range of the set would be "a-a^5", which makes it sufficient to answer. Can you please explain your reasoning.

Director
Joined: 25 Apr 2012
Posts: 721
Location: India
GPA: 3.21
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

18 May 2014, 06:21
2
KUDOS
ankit1101 wrote:
akhil911 wrote:
A set contains the following 5 numbers: a^2,a^5,a,a/2, and a/5. Is the range of the set equal to a^2–a^5?

1. a is negative
2. a^5<a

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C. Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Kudos me if you like the post !!!!

Hi Akhil

IMO it should be B.

As a^5 is less than a, it means that a is between 0 and 1. Hence range of the set would be "a-a^5", which makes it sufficient to answer. Can you please explain your reasoning.

For Statement 2, What if a < -1 In that case as well Range can be a^2> a^5 ??

Since there are 5 values it's important to make a table below

Attachment:

Untitled.png [ 14.35 KiB | Viewed 7143 times ]

Combining both statement you see that a is negative and a<-1

Ans is C
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Intern
Joined: 13 May 2014
Posts: 38
Concentration: General Management, Strategy
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

18 May 2014, 06:55
1
KUDOS
ankit1101 wrote:
akhil911 wrote:
A set contains the following 5 numbers: a^2,a^5,a,a/2, and a/5. Is the range of the set equal to a^2–a^5?

1. a is negative
2. a^5<a

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C. Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Kudos me if you like the post !!!!

Hi Akhil

IMO it should be B.

As a^5 is less than a, it means that a is between 0 and 1. Hence range of the set would be "a-a^5", which makes it sufficient to answer. Can you please explain your reasoning.

Hi Ankit,
It would be
[Reveal] Spoiler:
C.

There will be two cases for
a^5 < a
Case i) 0< a < 1 , which you pointed out; In this case a^5 will be even lesser fraction of the fraction a
Case ii) a < -1 ; in this case , a^5 and a both are negative numbers but a^5 is of higher magnitude than a

So,you see the statement 2 alone does not suffice to find out the range for the set which would differ in above both cases.

So, now checking each statement :
1) a is negative i.e a<0, for which range would be different for the cases
(i) if -1 <= a < 0
(ii) if a< -1 ; So,not sufficient

2) a^5<a for which range would be different for the cases
(i) if 0 < a <1
(ii) if a < -1 ; So,not sufficient

However,combining these two statements yield
a < -1, in which case we can find the range. Range would be a^2 - a^5

Kudos is the best form of appreciation
Non-Human User
Joined: 09 Sep 2013
Posts: 13791
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

17 Aug 2015, 20:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 07 Apr 2015
Posts: 179
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

31 Aug 2015, 04:26
1
KUDOS
Can anyone else give it a try? To be honest I still don't really understand it, even with the already posted solutions...
Current Student
Joined: 12 Aug 2015
Posts: 297
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

06 Dec 2015, 08:57
1
KUDOS
1
This post was
BOOKMARKED
basically this problem boils down to arranging the set in a single way. to do this we need to consider basic number properties. the stem says that the set can consist of any numbers: integers, fractions, positives, negatives - all those inputs would influence the order of the set. so we need to come to one possible interval of values to have an exclusive set

STATEMENT 1: says a is negative, but this cannot be sufficient to arrange our set in one exclusive way because the numbers can still be either integers or fractions (less than -1 or greater) or both and THUS the set could take any order. you can try several numbers to test this or draw a number line.

a<-1 or -1<a<0 produce different sets

STATEMENT 2: says that a is either less than -1 or between 0 and 1, i.e. any number less than -1 or a positive fraction between 0 and 1. again this can produce different sets hence not sufficient.

a^5-a<0 -> a(a-1)(a+1)(a^2+1)<0 -> hence for the inequality to be true -> a<-1 or 0<a<1 give different sets

1+2 = sufficient because now it explicitly says that a is a negative number less than -1 that is a<-1 and hence the set can be organized in a single fashion. you can try different numbers to test this. integers fractions.
_________________

KUDO me plenty

Retired Moderator
Joined: 18 Sep 2014
Posts: 1199
Location: India
A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

25 Mar 2016, 04:25
2
This post was
BOOKMARKED
A set contains the following 5 numbers: $$a^2, a^5, a, \frac{a}{2}, \frac{a}{5}$$. Is the range of the set equal to $$a^2 - a^5$$?

(1) a is negative
(2) $$a^5 < a$$

Concept as per OE is
Quote:
if a is a negative number such that $$-1 < a < 0$$ (in other words a negative proper fraction) then a will always be the smallest number and the range would be $$a^2–a$$.

I tried this way which looks simple enough to me.

Statement 1: a is negative number i.e., a can be -1, -2, ...........so on.

Let a=-1
The 5 no's will be
$$a^2=1,$$
$$a^5=-1,$$
$$a=-1,$$
$$\frac{a}{2}=\frac{-1}{2},$$
$$\frac{a}{5}=\frac{-1}{5}$$

Arranged order will be

$$-1, -1, -1/2, -1/5, 1$$ i.e.,

The order is
either $$a^5, a, \frac{a}{2}, \frac{a}{5}, a^2$$ giving us the range $$a^2 - a^5$$ and answer YES to the question.

or $$a, a^5, \frac{a}{2}, \frac{a}{5}, a^2$$ giving us the range $$a^2 - a$$ and answer NO to the question.

Since there is some uncertainty, we try the same procedure with a=-2

Arranged order will be

$$-32, -2, -1, -2/5, 4$$ i.e.,

The order is
$$a^5, a, \frac{a}{2}, \frac{a}{5}, a^2$$ giving us the range $$a^2 - a^5$$ and answer YES to the question.

Now we can say Statement 1 is not sufficient.

Statement 2: $$a^5 < a$$ this gives us the required hint that a cannot be -1 as above.

But this can be positive as well and be within (0, 1).

Thus Statement 2 is insufficient.

Combining both the statements we get the answer YES for all the values of a<-1.
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

Non-Human User
Joined: 09 Sep 2013
Posts: 13791
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

29 Apr 2017, 09:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Retired Moderator
Joined: 05 Jul 2006
Posts: 1747
A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

29 Apr 2017, 14:20
1
KUDOS
akhil911 wrote:
A set contains the following 5 numbers: $$a^2, a^5, a, \frac{a}{2}, \frac{a}{5}$$. Is the range of the set equal to $$a^2 - a^5$$?

(1) a is negative
(2) $$a^5 < a$$

the question is asking whether a^2 is the largest number in the set and whether a^5 is the smallest.

from 1

since a is -ve we know a^2 is largest but we cant be sure whether a^5 is smallest ( true if a is integer for example and false if a is a -ve fraction).. insuff

from 2

a^5< a .... a^5 - a < 0 , i.e. a(a^4 - 1) < 0 this is true if a is -ve and larger than 1 or a is a +ve fraction... insuff

both together

a is a -ve fraction larger than 1 thus surely range is a^2 - a^5
C
Manager
Joined: 17 Aug 2012
Posts: 172
Location: India
Concentration: General Management, Strategy
Schools: Copenhagen, ESMT"19
GPA: 3.75
WE: Consulting (Energy and Utilities)
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

25 Jun 2017, 00:28
A set contains the following 5 numbers: a2,a5,a,a2,a5a2,a5,a,a2,a5. Is the range of the set equal to a2−a5a2−a5?

(1) a is negative
(2) a5<a

For statement 1 . the set range is differenent when we select value less than - 1 and when we select value between -1 and 0
statement 2 a(a^4-1)< 0
a(a^2+1) (a+1)(a-1)<0
this will hold when a< -1 or a is between 0 an 1

combining statement 1 and 2
Intern
Joined: 29 May 2016
Posts: 11
Location: India
GMAT 1: 550 Q42 V25
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

### Show Tags

24 Sep 2017, 18:27
Unable to understand how 0<a<1 was conceived.

If a(a^4-1)< 0
a(a^2+1) (a+1)(a-1)<0

correct me if i am wrong ; a<0 else a<-1 else a<1
How do you get a is between 0 and 1 ??? ( i understand the portion a<-1)
Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the   [#permalink] 24 Sep 2017, 18:27
Display posts from previous: Sort by