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Source: — Data Sufficiency |

by GMATGuruNY » Sat Aug 02, 2014 2:53 am
[email protected] wrote:Is K a positive number?

(1) |K^3|+1>K

(2) K+1>|K^3|
Both statements are satisfied if k=0 or if k=1.
If k=0, then K is not positive.
If k=1, then K is positive.
Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Matt@VeritasPrep » Sat Aug 02, 2014 12:01 pm
A useful observation here: the first statement is true of ANY number. So S1 is totally useless, meaning the answer is either B or E.

The second statement has two cases.

Case I: k is nonnegative.

This gives us k + 1 > k³, or 1 > k³ - k, or 1 > k(k+1)(k-1). This is true if k = 0 or k+1 = 0 (among other possibilities), so S2 is INSUFFICIENT.

Just for fun, the second case gives us

Case II: k is negative, or k+1 > -k³, which obviously has a few solutions itself.
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by GMATinsight » Mon Aug 04, 2014 6:53 am
[email protected] wrote:Is K a positive number?

(1) |K^3|+1>K

(2) K+1>|K^3|
Solution :

Question : Is K > 0 ?

Statement 1) |K^3|+1>K

i.e. |K^3|+1>K
i.e. +K^3 + 1 > K
i.e. +K^3 + 1 > K OR i.e. -K^3 + 1 > K
i.e. K can be 0.5 or K can be -0.5
NOT SUFFICIENT

Statement 2) K+1>|K^3|
i.e. K can be 0.5 or K can be -0.5
NOT SUFFICIENT

Combining the two statements
i.e. K can be 0.5 or K can be -0.5
NOT SUFFICIENT

Answer: Option E
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