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

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Math Expert
Joined: 02 Sep 2009
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Is the two digit integer k less than or equal to 19?  [#permalink]

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09 Dec 2019, 00:21
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Difficulty:

45% (medium)

Question Stats:

64% (01:35) correct 36% (01:27) wrong based on 27 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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Is the two digit integer k less than or equal to 19?  [#permalink]

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09 Dec 2019, 08:38
Bunuel wrote:
Is the two digit integer k less than or equal to 19?

(1) k^2 > 400

(2) k^3 < 8000

Are You Up For the Challenge: 700 Level Questions

Analyzing the question:
Note we are only given that k is a two-digit integer, it might be negative.

Statement 1:
This simplifies to $$| k | > 20$$, which is either $$k > 20$$ or $$k < -20$$. Therefore k might be greater than 19 or less, insufficient.

Statement 2:
$$k ^ 3 < 8000, k ^3 < 20 ^ 3, k < 20.$$

k must be 19 at most, so it is indeed less than or equal to 19. Sufficient.

Ans: B
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Is the two digit integer k less than or equal to 19?   [#permalink] 09 Dec 2019, 08:38
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