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Is a^2 > 3a – b^4?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Aug 21, 2018 10:19 pm
BTGmoderatorDC wrote:Is a^2 > 3a - b^4?

(1) 3a - b^4 = -5
(2) a > 5 and b > 0

OA D

Source: Veritas Prep
Let's take each statement one by one.

(1) 3a - b^4 = -5

=> The question rephrased to: Is a^2 > -5?

Since a^2 is a non-negative number, a^2 > -5. Sufficient.

(2) a > 5 and b > 0

We have: Is a^2 > 3a - b^4?

=> a^2 -3a > -b^4
=> a(a - 3) > -b^4

Since a > 5, we have (a - 3) > 2

Thus, a(a - 3) is positive.

Since given b > 0, we have b^4 is a positive number.

Thus, -b^4 is a negative number.

=> a(a - 3) > -b^4. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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