If x = -(0.2)^(200), then x satisfies which of the following

Question

If  x = -\sqrt {0.2} , then  x  satisfies which of the following inequalities?

A.  x < -1 
B.  -1 < x < -0.9 
C.  -0.9 < x < -0.5 
D.  -0.5 < x < -0.1 
E.  -0.1 < x < 0

Bunuel · Accepted Answer

Official Solution:

If  x = -\sqrt {0.2} , then  x  satisfies which of the following inequalities?

A.  x < -1 
B.  -1 < x < -0.9 
C.  -0.9 < x < -0.5 
D.  -0.5 < x < -0.1 
E.  -0.1 < x < 0

x = -\sqrt {0.2} =

= -\sqrt {\frac{1}{5}} =

= -\frac{1}{\sqrt {5}}

Such a large root from 5 would still be more than 1, however very close to it. Therefore:

-\frac{1}{\sqrt {5}}\approx

\approx -\frac{1}{1.001}

Finally,  -\frac{1}{1.001}  will be more than -1, however very close to it.

Answer: B

gmatophobia · Answer

Assume

x^1 = 0.2 ⇒ x = 0.2

Let's see the effect of increasing the power on x. Assume the power on  x  was 2

x^2 = 0.2 ⇒ x = \sqrt {0.2} = \pm \sqrt {\frac{2}{10}}

=\pm \frac{\sqrt {2}}{\sqrt {10}}   \approx \pm \frac{1.5}{3} \approx \pm {0.5}

So we see that the value of power on x increases, and the value of x increases.

i.e
 
 when the power = 1 ⇒  x = 0.2  
 when the power = 2 ⇒  x \approx 0.5

x = -\sqrt {0.2}

Raising to the power of 200 on both sides

x^{200} = 0.2

From our analysis above we can conclude that x is either greater than 0.5 or less than -0.5. Hence, we can eliminate D and E. The value will not exceed 1 or be less than -1 because the root value will not be in decimals in that case. Hence, eliminate A.

Between B and C, we can infer that the value of x would be a value very close to 1 or -1

As we have a negative sign in the question, the value will be very close to -1

Option B

Oppenheimer1945 · Answer

-x is (0.2)^1/z
z=200.

For z=1, -x is 0.2
For z=2, -x is -0.45

For z =very large number say infinity, -x is (0.2)^0=1

Hence -x would be very close to 1 for z=200

x should be close to -1 & -0.9

Posted from my mobile device

Elite097 · Answer

KarishmaB  how can we infer that it will be very close to -1 and not something like -0.8 in choice C ?

Posted from my mobile device

KarishmaB · Answer

Numbers in the range 0 to 1, when taken under the radical sign will move towards 1 but never reach it. 
Square root of 1/4 is 1/2 = .5 (closer to 1) 
Cube root of 1/4  is .63 (closer to 1) 
Fourth root of 1/4 is 0.7 (even closer to 1)
and so on...
When you take 0.2 under the radical sign, it will move towards 1 too. With a number as large as 200, the value will be almost 1 though not quite. I would worry if it was the sixth root or something of 0.2. Since they have given you outright 200, you know that they are messing around. It has to be almost 1.
What they are saying is - if we take a big big root of a number between 0 and 1, what will be its value? It will be almost 1. Hence in teh question x will be a tiny tiny bit greater than -1. 
Answer (B)
I have discussed these relations in my Exponents and Roots module. You can access it for free tomorrow under the Super Sundays program. Check  this video  on my YouTube channel for details.

bumpbot · Answer

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If x = -(0.2)^(200), then x satisfies which of the following

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If x = -(0.2)^(200), then x satisfies which of the following

Prep Toolkit

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