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Which of the following is the closest value of x such that

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Which of the following is the closest value of x such that  [#permalink]

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New post 07 Jun 2017, 00:23
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Which of the following is the closest value of x such that \(x^{20}+x^2+0.0000019=0.09\)?

A. 0.1
B. 0.01
C. 0.3
D. 0.03
E. 0.003

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Re: Which of the following is the closest value of x such that  [#permalink]

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New post 07 Jun 2017, 00:36
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MathRevolution wrote:
Which of the following is the closest value of x such that \(x^{20}+x^2+0.0000019=0.09\)?
A. 0.1
B. 0.01
C. 0.3
D. 0.03
E. 0.003


\(x^{20}+x^2+0.0000019=0.09\)

Nice Question
Rather than testing options, one of the best way to solve the solve is to reduce the variables
\(x^{20}+x^2+0.0000019=0.09\)
Reduced to
\(x^2+0.0000019=0.09\)
Reduced to
\(x^2=0.09\)

Voila, x = 0.3

Answer C
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Which of the following is the closest value of x such that  [#permalink]

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New post 07 Jun 2017, 07:12
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MathRevolution wrote:
Which of the following is the closest value of x such that \(x^{20}+x^2+0.0000019=0.09\)?

A. 0.1
B. 0.01
C. 0.3
D. 0.03
E. 0.003


When a GMAT question tells us to find the "closest value" or the "approximate value," this usually gives us the go ahead to estimate.

First recognize that, for all 5 answer choices, the value of x^20 becomes inconsequential
For example, if x = 0.1, then x^20 = (0.1)^20 = (1/10)^20 = 1/100000000000000000000
The same applies to all 5 answer choices.

Since the value of x^20 has almost no effect on the equation, we can safely ignore it.

Likewise, the value 0.0000019 is very very very small in relation to 0.09
So, we can safely ignore it.

So, our equation becomes x² ≈ 0.09
Solve to get: x ≈ 0.3

Answer:

Cheers,
Brent
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Re: Which of the following is the closest value of x such that  [#permalink]

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New post 09 Jun 2017, 01:35
==> From \(x^{20}+x^2+0.0000019=0.09, x^{20}\) and 0.0000019 are very close to 0, so you can ignore them, and the equation becomes \(x^2=0.09=0.3^2\). Thus, you get x=0.3.

The answer is C.
Answer: C
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Re: Which of the following is the closest value of x such that  [#permalink]

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New post 09 Jun 2017, 07:41
Imo C we can do this question by approximations
Ignore x^20 and 0.0000019
Thus we have
X^2 =0.09
0.3 is our answer

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Re: Which of the following is the closest value of x such that  [#permalink]

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