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

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Manager
Joined: 07 Apr 2018
Posts: 107
Is the two digit integer k less than or equal to 19?  [#permalink]

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08 Jun 2018, 05:16
00:00

Difficulty:

45% (medium)

Question Stats:

64% (00:36) correct 36% (01:21) wrong based on 22 sessions

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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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Manager
Joined: 24 Jun 2013
Posts: 98
Re: Is the two digit integer k less than or equal to 19?  [#permalink]

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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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Director
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Joined: 01 Oct 2017
Posts: 505
WE: Supply Chain Management (Energy and Utilities)
Re: Is the two digit integer k less than or equal to 19?  [#permalink]

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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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PKN

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