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03 Sep 2023, 05:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
26% (01:57) correct
74%
(02:46)
wrong
based on 35
sessions
History
Date
Time
Result
Not Attempted Yet
03 Sep 2023, 10:15
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Bunuel
Let us simplify or modify the question.
\(5b(a+b)>-a^2-b^2\)
\(5ba+5b^2>-a^2-b^2\)
\(a^2+6b^2+5ab>0\)
\(a^2+4b^2+4ab+2b^2+ab>0\)
\((a+2b)^2+b(a+2b)>0\)
\((a+2b)(a+2b+b)>0\)
The question is: Is \((a+2b)(a+3b)>0\)?
Two cases, the answer will be yes
(A) Both a+2b and a+3b are positive.
As b is negative, a+2b>a+3b.
Thus, knowing a+3b>0 is sufficient
(B) Both a+2b and a+3b are negative.
As b is negative, a+2b>a+3b.
Thus, knowing a+2b<0 is sufficient
Let us check the statements
(1) \(a+2b>0\)
Nothing about a+3b.
(2) \(a+3b>0\)
Sufficient
B
An example
Say a=5, b=-2, then a+2b>0 but a+3b<0.
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