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

Question

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

kunalcvrce · Answer

Since square of any term is greater than negative so x^2 will always be greatest only option 3

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GMATinsight · Answer

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

Answer: Option C

aggvipul · Answer

X^2 is the biggest value here, hence option C

Abhishek009 · Answer

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)

ScottTargetTestPrep · Answer

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. Answer: C

Funsho84 · Answer

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.

C is the answer

Stutimahap · Answer

X3< x < x2 should be the correct option

manavkothari · Answer

Exactly how come x^3 is getting larger than x as x^3 will be negative and and a much smaller number than x. I think there is an error in the answers and none of the options are correct.

GraemeGmatPanda · Answer

x^3 is larger than x because the number is between -1 and 0.

To illustrate, if you take for example if x = -0.1, x^3 would be -0.001 which is bigger than x

x^3 = \left(\frac{-1}{20}ight)^3 = -\frac{1}{8000}

x^2 = \left(\frac{-1}{20}ight)^2 = \frac{1}{400}

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

x < x^3 < x^2

Answer Only statement III is true.

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

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GMAT Problem Solving (PS) Questions

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

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