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

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

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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

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Last edited by Nevernevergiveup on 25 Mar 2016, 04:55, edited 3 times in total.
Edited the question and original answer was incorrect.

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

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New post 18 May 2014, 06:13
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
D. EACH statement ALONE is sufficient to answer the question asked
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


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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.

Thanks in advance.

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

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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
D. EACH statement ALONE is sufficient to answer the question asked
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed


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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.

Thanks in advance.


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
Untitled.png [ 14.35 KiB | Viewed 6485 times ]


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

Ans is C
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Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the [#permalink]

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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
D. EACH statement ALONE is sufficient to answer the question asked
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.

Thanks in advance.


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

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

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

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Can anyone else give it a try? To be honest I still don't really understand it, even with the already posted solutions...

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

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

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

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

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

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New post 25 Jun 2017, 01:28
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
answer is C

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

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New post 24 Sep 2017, 19:27
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)

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Re: A set contains the following 5 numbers: a^2, a^5, a, a/2, a/5. Is the   [#permalink] 24 Sep 2017, 19:27
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