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What is the value of k?

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What is the value of k?  [#permalink]

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New post Updated on: 25 Sep 2016, 06:52
3
5
00:00
A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:04) correct 49% (00:53) wrong based on 129 sessions

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What is the value of k?

(1) \(k^4 = \frac{1}{625}\)
(2) \(k^3 < k^2\)

Originally posted by Nevernevergiveup on 25 Sep 2016, 05:10.
Last edited by Nevernevergiveup on 25 Sep 2016, 06:52, edited 2 times in total.
Renamed the topic, edited the question and tags.
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Re: What is the value of k?  [#permalink]

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New post 25 Sep 2016, 05:49
1
(1) \(K^4 = \frac{1}{625}\)

\(K^4\) =\(5^{-4}\)

==> k= \(5^{-1}\)= \(\frac{1}{5}\) or k =\(- \frac{1}{5}\) --Not Sufficient

(2) \(k^3 < K ^2\) -- Not sufficient

Lets combine (1) and (2).

\(k^3 < K ^2\) ==> \((- \frac{1}{5} )^3 < (- \frac{1}{5} )^2 ==> - \frac{1}{125} < \frac{1}{25}\) --True

\(k^3 < K ^2\) ==> \(( \frac{1}{5} )^3 < (- \frac{1}{5} )^2 ==> \frac{1}{125} < \frac{1}{25}\) --True

Ans E.
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What is the value of k?  [#permalink]

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New post 25 Sep 2016, 11:27
1
Nevernevergiveup wrote:
What is the value of k?

(1) \(k^4 = \frac{1}{625}\)
(2) \(k^3 < k^2\)

(1) K=1/5 or -1/5 .....not sufficient

(2)K^3-K^2<0
K^2(K-1)<0--------->K-1<0------->K<1.......not suff...

Combining again as K<1 (from 2)
K=1/5 or -1/5 .....not suff

Ans E
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Re: What is the value of k?  [#permalink]

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New post 23 Feb 2017, 04:48
SUPER SET
The value of k will be a real number.

TRANSLATION
In order to find the value, we need:
Exact value of k.
Any equation to solve for k.
Any characteristics of k.

STATEMENT ANALYSIS
St 1: k^4=1/625
k^4-1/625 = 0
k^4- ⅕^4 = 0
(k^2+1/25)(k +⅕)(k-⅕) = 0
Therefore k = ⅕, -⅕
INSUFFICIENT. Hence option a and d eliminated.

St 2: k^3<k^2, holds for infinite values of k. INSUFFICIENT. Hence option b eliminated.

St 1 & St 2: From St 1, we got k = ⅕, -⅕. Putting these values in the equation from St 2, we get k = -⅕ as well as ⅕ holds true for the equation. HEnce INSUFFICIENT. Option C eliminated.

Hence option E
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Re: What is the value of k ?  [#permalink]

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New post 15 Mar 2018, 05:44
SonalSinha803 wrote:
What is the value of k ?

1. k ^ 4 = 1/625

2. k ^ 3 < k ^ 2

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IMO E.

Statement 1) \(k^4 = 1/625\)
-> \(k^2 = 1/25\) ( taking square root and neglecting the negative value)
-> \(k = +- 1/5\) ( taking sq root)

Not sufficient.

Statement 2) \(k^3 < k^2\)

This could be true in two cases - 1) k is negative. So k cube is negative while k square is positive.
2) k is positive and between 0 and 1. Increasing powers of k become smaller.
Not sufficient.

(1) and (2) together are also insufficient.

Hence E.

Please give kudos if you liked my explanation...
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Re: What is the value of k ?  [#permalink]

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New post 15 Mar 2018, 07:00
1
PraveenChahal wrote:
.

Combining the two equations is still insufficient as..

+1/5 and -1/5 could both be k.
We need to zero down to one possibility.

Hope that solved your question.

Kindly give Kudos if you liked my post...
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Re: What is the value of k ?  [#permalink]

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New post 15 Mar 2018, 07:08
Hi,

What I did with the second option is

k^3 - k^2 = k^2(k - 1) < 0

Thus, k < 0 or k < 1

Where am I wrong...please do explain.

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Re: What is the value of k ?  [#permalink]

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New post 15 Mar 2018, 07:29
SonalSinha803 wrote:
Hi,

What I did with the second option is

k^3 - k^2 = k^2(k - 1) < 0

Thus, k < 0 or k < 1

Where am I wrong...please do explain.

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app


SonalSinha803
Your result is correct. What do you infer from that? K could have both values of +1/5 and -1/5 ( also considering the info from statement 1) so both statements are not sufficient.

Does that make sense?
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What is the value of k ?  [#permalink]

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New post 15 Mar 2018, 07:40
hi
Your interpretation should be only interpretation will be k<1. it will automatically cover x<0 :cool:
So it will cover both 1/5 and -1/5 ( as both are less than 1).
hence it is not sufficient.

Hence E.


SonalSinha803 wrote:
Hi,

What I did with the second option is

k^3 - k^2 = k^2(k - 1) < 0

Thus, k < 0 or k < 1

Where am I wrong...please do explain.

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app

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Re: What is the value of k?  [#permalink]

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New post 15 Mar 2018, 10:44
Thankyou everyone....I realised I made a silly mistake.

Thankyou for the clarity [GRINNING FACE WITH SMILING EYES]

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Re: What is the value of k? &nbs [#permalink] 15 Mar 2018, 10:44
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