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Is 2a < a^2 + b? (1) 0 < a < 2 (2) -2 < b < 0

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Princ
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Is 2a < a^2 + b? (1) 0 < a < 2 (2) -2 < b < 0 [#permalink] New post   26 Oct 2018, 10:33
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45% (medium)

Question Stats:

65% (01:33) correct 35% (01:46) wrong based on 75 sessions
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Is \(2a < a^2 + b\) ?

(1) \(0 < a < 2\)
(2) \(-2 < b < 0\)
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C
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BrentGMATPrepNow
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Re: Is 2a < a^2 + b? (1) 0 < a < 2 (2) -2 < b < 0 [#permalink] New post   26 Oct 2018, 11:35
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Princ wrote:
Is \(2a < a^2 + b\) ?

(1) \(0 < a < 2\)
(2) \(-2 < b < 0\)


Target question: Is 2a < a² + b

Statement 1: 0 < a < 2
No information about b, so statement 1 is NOT SUFFICIENT

Statement 2: -2 < b < 0
No information about a, so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
It may help to REPHRASE the target question by getting the a's on one side of the equation
Take: Is 2a < a² + b?
Subtract a² from both sides to get: Is 2a - a² < b?
Factor left side to get: Is a(2 - a) < b?

Since 0 < a < 2, we know that a is POSITIVE, and we know that (2 - a) is POSITIVE
Also, if -2 < b < 0, then we know that b is NEGATIVE

So, our target question becomes: Is (POSITIVE)(POSITIVE) < NEGATIVE?
Simplify left side to get: Is POSITIVE < NEGATIVE?
The answer to this REPHRASED question is "NO, it is definitely NOT the case that POSITIVE < NEGATIVE"
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Florentina123
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Re: Is 2a < a^2 + b? (1) 0 < a < 2 (2) -2 < b < 0 [#permalink] New post   20 Jan 2024, 11:16
We are not told that a,b are integers though? a,b could be a fraction therefore we get yes and no to both statements; the correct answer should be E?
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Re: Is 2a < a^2 + b? (1) 0 < a < 2 (2) -2 < b < 0 [#permalink] New post   20 Jan 2024, 11:38
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Florentina123 wrote:
We are not told that a,b are integers though? a,b could be a fraction therefore we get yes and no to both statements; the correct answer should be E?



You will get answer no irrespective of the variables being integer or fraction.
Please share how you get E, so that the query could be addressed properly
GMAT Club Bot
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Re: Is 2a < a^2 + b? (1) 0 < a < 2 (2) -2 < b < 0 [#permalink]
20 Jan 2024, 11:38
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Bunuel
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