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Is the two digit integer k less than or equal to 19?

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Joined: 07 Apr 2018
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Is the two digit integer k less than or equal to 19? [#permalink]

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New post 08 Jun 2018, 05:16
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Is the two digit integer k less than or equal to 19?

(1) K^2 > 400

(2) K^3 < 8000

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Re: Is the two digit integer k less than or equal to 19? [#permalink]

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New post 08 Jun 2018, 10:39
PP777 wrote:
Is the two digit integer k less than or equal to 19?

(1) K^2 > 400

(2) K^3 < 8000


stat 1 ==> remember the notion \(\sqrt{x^2}= |x|\)

so taking sqrt , stat 1 becomes |K|>20 which states two cases either K > 20 or K < -20 , two solution hence insuff

Stat2 ==> taking cube rt , we have k< 20 hence the answer ... suff
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Re: Is the two digit integer k less than or equal to 19? [#permalink]

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New post 08 Jun 2018, 20:54
PP777 wrote:
Is the two digit integer k less than or equal to 19?

(1) K^2 > 400

(2) K^3 < 8000


Given, K is a two digit integer.

Question stem:- Is K<19 or K=19 ? (Y/N)

St1, \(K^2\)>\(20^2\)
Or, |K|>20
So when K>20, Is K<19 or K=19? No
when K<-20, Is Is K<19 or K=19? Yes

So, St1 is not sufficient.

St2, K\(^3 < 20^3\)
Or, \(K^3-20^3<0\)
Or, \((K-20)(K^2+20K+20^2)<20\)
Or, (K-20)<0 or K<20 (since \(K^2+20K+20^2\) yields imaginary roots, hence we are not interested)
hence K<20. So, two digit integer K is less than or equal to 19.

So st2 is sufficient.

Ans B
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Re: Is the two digit integer k less than or equal to 19?   [#permalink] 08 Jun 2018, 20:54
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Is the two digit integer k less than or equal to 19?

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