What is x?
(1) y = x^3-1
(2) y=x-1
Equations
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the algebraic formula here is:
a^3-b^3 = (a-b)(a^2+ab+b^2)
x^3-1 = (x-1)(x^2+x+1)
statement(1): y = x^3-1, alone is not suff
statement(2): y = x-1, alone is not suff
considering both the statements,
x^3-1 = x-1
=>(x-1)(x^2+x+1) = x-1
=>(x-1)(x^2+x+1-1)=0
=>(x-1)(x^2+x)=0
=>(x-1)x(x+1)=0
=> x = 0,1,-1 => x has got three values, the is ambiguity
even if we consider two statements, there is no clarity on x value
Answer "E"
a^3-b^3 = (a-b)(a^2+ab+b^2)
x^3-1 = (x-1)(x^2+x+1)
statement(1): y = x^3-1, alone is not suff
statement(2): y = x-1, alone is not suff
considering both the statements,
x^3-1 = x-1
=>(x-1)(x^2+x+1) = x-1
=>(x-1)(x^2+x+1-1)=0
=>(x-1)(x^2+x)=0
=>(x-1)x(x+1)=0
=> x = 0,1,-1 => x has got three values, the is ambiguity
even if we consider two statements, there is no clarity on x value
Answer "E"
RaviSankar Vemuri
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It is obvious that each statement individually is not sufficient as we don't have any idea about y. But both statements taken together we can eliminate y as and write (x³ - 1) = (x - 1)kullayappayenugula wrote:What is x?
(1) y = x³-1
(2) y=x-1
So, (x³ - 1) = (x - 1)
--> (x³ - 1) - (x - 1) = 0
--> (x³ - x) = 0
--> x(x² - 1) = 0
--> x(x - 1)(x + 1) = 0
Hence, x can be either -1 or 0 or 1.
Not sufficient
The correct answer is E.
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