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If x=0.2, then what is the value of x^3-1/x-1?

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If x=0.2, then what is the value of x^3-1/x-1?  [#permalink]

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New post 12 Feb 2019, 01:08
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[GMAT math practice question]

If \(x=0.2\), then what is the value of \(\frac{x^3-1}{x-1}\)?

\(A. 1.2\)
\(B. 1.22\)
\(C. 1.24\)
\(D. 1.44\)
\(E. 2.22\)

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If x=0.2, then what is the value of x^3-1/x-1?  [#permalink]

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New post 12 Feb 2019, 01:12
0.2 = 2/10. \(x^3\) = \(\frac{8}{1000}\)
\(x^3-1\) = \(\frac{-992}{1000}\)

\(x-1 = \frac{-8}{10}\)

\(\frac{(x^3-1)}{(x-1)}\) = \(\frac{992}{1000}*\frac{10}{8}\) = 124/100 = 1.24

C is the answer.
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Re: If x=0.2, then what is the value of x^3-1/x-1?  [#permalink]

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New post 12 Feb 2019, 01:17
MathRevolution wrote:
[GMAT math practice question]

If \(x=0.2\), then what is the value of \(\frac{x^3-1}{x-1}\)?

\(A. 1.2\)
\(B. 1.22\)
\(C. 1.24\)
\(D. 1.44\)
\(E. 2.22\)



x = 0.02


Given ,

\(\frac{x^3-1}{x-1}\)

= \(0.2^3\)- 1 / 0.2 - 1

= 0.008 - 1 / - 0.8

= - 0.992 / - 0.8

= 1.24.


The best answer is C.
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If x=0.2, then what is the value of x^3-1/x-1?  [#permalink]

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New post Updated on: 13 Feb 2019, 22:34

Solution



Given:
    • The value of x = 0.2

To find:
    • The value of the expression \(\frac{x^3 – 1}{x – 1}\)

Approach and Working:
We know that
    • \(x^3 – 1 = (x – 1) (x^2 + x + 1)\)

Therefore, \(\frac{x^3 – 1}{x – 1} = x^2 + x + 1\)

Now, if x = 0.2
    • The value of the given expression = \((0.2)^2 + 0.2 + 1 = 0.04 + 0.2 + 1 = 1.24\)

Hence, the correct answer is option C.

Answer: C


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Originally posted by EgmatQuantExpert on 12 Feb 2019, 02:36.
Last edited by EgmatQuantExpert on 13 Feb 2019, 22:34, edited 1 time in total.
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Re: If x=0.2, then what is the value of x^3-1/x-1?  [#permalink]

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New post 12 Feb 2019, 21:09
MathRevolution wrote:
[GMAT math practice question]

If \(x=0.2\), then what is the value of \(\frac{x^3-1}{x-1}\)?

\(A. 1.2\)
\(B. 1.22\)
\(C. 1.24\)
\(D. 1.44\)
\(E. 2.22\)


((0.2)^3 - 1)/(0.2 - 1)

(0.008 - 1)/(-0.8)

(-0.992)/(-0.8) = 1.24

Alternate solution:

The formula for factoring the difference of cubes is (x^3 - 1) = (x - 1)(x^2 + x +1). We can use that fact to simplify (x^3 - 1)/(x - 1) = x^2 + x + 1. Therefore, when x = 0.2, we have:

(0.2)^2 + 0.2 + 1 = 0.04 + 0.2 + 1 = 1.24

Answer: C
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Re: If x=0.2, then what is the value of x^3-1/x-1?  [#permalink]

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New post 14 Feb 2019, 02:02
=>


\(\frac{x^3-1}{x-1} = \frac{(x-1)(x^2+x+1)}{x-1}= x^2+x+1\)

Plugging in \(x = 0.2\) yields
\(x^2+x+1 = (0.2)^2 + (0.2) + 1 = 0.04 + 0.2 + 1 = 1.24\)

Therefore, the answer is C.
Answer: C
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Re: If x=0.2, then what is the value of x^3-1/x-1?   [#permalink] 14 Feb 2019, 02:02
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