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26 Oct 2018, 10:33
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:38) correct
36%
(01:50)
wrong
based on 100
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(2a < a^2 + b\) ?
(1) \(0 < a < 2\)
(2) \(-2 < b < 0\)
(1) \(0 < a < 2\)
(2) \(-2 < b < 0\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
26 Oct 2018, 11:35
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Princ
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
20 Jan 2024, 11:16
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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?
