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13 Feb 2019, 09:55
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C
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Difficulty:
85%
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Question Stats:
55% (02:38) correct
45%
(02:23)
wrong
based on 235
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If \(a* = a – a^2\) for all values of a, what is the value of b*?
(1) \((b + 1)* = –12\)
(2) \((b − 3)* = 0\)
(1) \((b + 1)* = –12\)
(2) \((b − 3)* = 0\)
13 Feb 2019, 11:02
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PeepalTree
To find b* we need to either know the value of b itself, or the value of b-b^2
(1) (b+1)* = -12. Then b+1 - (b^2+2b+1) = -12 and -b^2-b=-12 and b^2+b=12 and b^2+b-12 =0, thus (b+4)(b-3) = 0 so b=-4 or b=3 NS
(2) (b-3)* = 0, so b-3 -(b^2-6b+9) =0 therefore -b^2+7b-12 =0 and b^2-7b+12=0, so (b-4)(b-3) =0 so b=4 or b=3 NS
(1) and (2) b=-4 or b=3 AND b=4 or b=3 Therefore b must =3, thus b* = 3-3^2 = -6 Sufficient. Answer is C
13 Feb 2019, 22:11
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Solution
Given:
- • The function a* is defined as a – a^2, for all values of a
To find:
- • The value of b*
Analysing Statement 1
As per the information given in statement 1, (b + 1)* = -12
Simplifying this as per the function definition, we get
- • (b + 1)* = -12
Or, (b + 1) – (b + 1)^2 = -12
Or, (b + 1) – (b^2 + 2b + 1) = -12
Or, b^2 + b – 12 = 0
Or, b^2 + 4b – 3b – 12 = 0
Or, (b + 4) (b – 3) = 0
Or, b = -4 or 3
As we cannot determine the exact value of b, statement 1 is not sufficient to answer the question.
Analysing Statement 2
As per the information given in statement 2, (b – 3)* = 0
Simplifying this as per the function definition, we get
- • (b – 3)* = 0
Or, (b – 3) – (b – 3)^2 = 0
Or, (b – 3) – (b^2 – 6b + 9) = 0
Or, b^2 – 7b – 12 = 0
Or, b^2 – 4b – 3b – 12 = 0
Or, (b – 4) (b – 3) = 0
Or, b = 4 or 3
As we cannot determine the exact value of b, statement 2 is not sufficient to answer the question.
Combining Both Statements
From statement 1,
- • The possible values of b = -4 or 3
- • The possible values of b = 4 or 3
Therefore, combining both statements, we can say b = 3
So, b* = 3 - 3^2 = 3 - 9 = -6
Hence, the correct answer is option C.
Answer: C
