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DS - Inequality

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by karthikpandian19 » Sat Jul 07, 2012 8:13 pm
Is 9a - 5b < a^4?

9a - 5b = -7
a > 3 and b > 0.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sat Jul 07, 2012 8:28 pm
karthikpandian19 wrote:Is 9a - 5b < a^4?

(1) 9a - 5b = -7
(2) a > 3 and b > 0.
Note that a^4 is always greater than or equal to zero.

Statement 1: (9a - 5b) is negative.
Hence, (9a - 5b) must be less than a^4

Sufficient

Statement 2: As a > 3, a^4 > 9a for all possible values of a.
Hence, (a^4 - 9a) > 0
As b > 0, 5b > 0 ----> -5b < 0

So, -5b < 0 < (a^4 - 9a)
--> -5b < (a^4 - 9a)
--> (9a - 5b) < a^4

Sufficient

The correct answer is D.
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