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# If x = -1/20, which of the following is true?

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If x = -1/20, which of the following is true?  [#permalink]

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29 Mar 2018, 23:33
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If $$x = -\frac{1}{20}$$, which of the following is true?

I. $$x < x^2 < x^3$$

II. $$x^2 < x < x^3$$

III. $$x < x^3 < x^2$$

(A) I. only
(B) II. only
(C) III only
(D) I and II only
(E) II and III only

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Re: If x = -1/20, which of the following is true?  [#permalink]

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29 Mar 2018, 23:42
Since square of any term is greater than negative so x^2 will always be greatest only option 3

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Re: If x = -1/20, which of the following is true?  [#permalink]

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30 Mar 2018, 07:00
Bunuel wrote:
If $$x = -\frac{1}{20}$$, which of the following is true?

I. $$x < x^2 < x^3$$

II. $$x^2 < x < x^3$$

III. $$x < x^3 < x^2$$

(A) I. only
(B) II. only
(C) III only
(D) I and II only
(E) II and III only

This case is far more simpler because we already have the specific value to square and cube for comparison

However the rules go like this

1) Any value between 0 and 1 becomes smaller for higher powers and becomes a bigger number for smaller powers

2) In number is between 0 and -1 then any even power of it will make it positive and higher odd power will make it bigger than number

So here x^2 must be biggest and x must be smallest

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Re: If x = -1/20, which of the following is true?  [#permalink]

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30 Mar 2018, 07:17
X^2 is the biggest value here, hence option C
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Re: If x = -1/20, which of the following is true?  [#permalink]

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30 Mar 2018, 08:33
Bunuel wrote:
If $$x = -\frac{1}{20}$$, which of the following is true?

I. $$x < x^2 < x^3$$

II. $$x^2 < x < x^3$$

III. $$x < x^3 < x^2$$

(A) I. only
(B) II. only
(C) III only
(D) I and II only
(E) II and III only

$$x$$ $$=$$ $$-\frac{1}{20}$$
$$x^2$$ $$=$$ $$\frac{1}{400}$$
$$x^3$$ $$=$$ $$\frac{1}{8000}$$

Thus, $$x < x^3 < x^2$$ or, $$-\frac{1}{20}$$ < $$\frac{1}{8000}$$ < $$\frac{1}{400}$$, Answer must be (C)
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Re: If x = -1/20, which of the following is true?  [#permalink]

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04 Apr 2018, 17:23
Bunuel wrote:
If $$x = -\frac{1}{20}$$, which of the following is true?

I. $$x < x^2 < x^3$$

II. $$x^2 < x < x^3$$

III. $$x < x^3 < x^2$$

(A) I. only
(B) II. only
(C) III only
(D) I and II only
(E) II and III only

Since x is a negative proper fraction, we know that x^2 > x and that x^3 > x. Furthermore since x^2 is positive, x^2 > x^3. Thus:

x < x^3 < x^2

Alternate Solution:

We know that x^2 is the only positive value of the three, and so it has the largest value. Thus, only Roman numeral III can be true.

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Re: If x = -1/20, which of the following is true?  [#permalink]

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05 Apr 2018, 14:54
This question can be answered in 5 seconds by recognizing that X^2 will be a positive number. X and X^3 will remain negative.

Re: If x = -1/20, which of the following is true?   [#permalink] 05 Apr 2018, 14:54
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