If 0

Question

If 0 < x < 1, which of the following is the greatest?

A.  x^{(-\frac{1}{2})}

B.  x^0

C.  x^{(\frac{1}{2})}

D.  x^1

E.  x^2

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APram · Answer

Consider x=1/2

A) x^(-1/2) =  \sqrt{2} =1.414

B) x^0 = 1

C) x^(1/2)=  1/\sqrt{2}  = 1/1.414 < 1

D) x = 0.5

E) x^2 = 0.25

Hence  option A  is greatest

ManifestDreamMBA · Answer

Thinking of it logically
We have, 0 < x < 1

Given x is a fraction, non-zero exponents make it smaller 
Eliminates D and E

x^{(\frac{1}{2})}  will a fraction greater than the original fraction but less than  x^0 , which is equal to 0. Eliminates C

x^{(-\frac{1}{2})}  will be a number greater than 1, eliminates B

Answer A

Dereno · Answer

A number x between 0 and 1 is a fraction of the form p/q , where denominator q > numerator p.

let’s look Into the options

A.  x^{(-\frac{1}{2})}

x^-(1/2) =. 1/ (x)^1/2 = 1/sqrt(x) = sqrt (q/p) .

With denominator (q) greater than numerator (p). Sqrt (q/p) provides a value greater than 1.

B.  x^0

Any number to the power of zero “0” is 1.

C.  x^{(\frac{1}{2})}

square root of a number less than 1 cannot be greater than 1.

D.  x^1

This value is same as x, and lies between 0 < x <1.

E.  x^2

When we square a fraction, the value becomes less than the fraction.

Hence, the greatest value is Option A

rohitz98 · Answer

Given 0<x<1
taking x to be 1/2 and evaluating all options

A) x^(-1/2) gives sqrt(2) = 1.414
B) x^0 gives = 1
C) x^(1/2) gives = 1/sqrt(2)
D)x^1 gives 0.5
E)x^2 gives 0.25

Hence  Option A  is the answer

GraemeGmatPanda · Answer

Always a classic!

Another way to think about this one is to use the property of exponents for numbers between 0 and 1.
\(0 < x < 1,\; m > n \implies x^m < x^n\)

Identify all the exponents in the options.
\(\text{Exponents are } -\frac{1}{2},\;0,\;\frac{1}{2},\;1,\;2\)

Arrange these exponents from largest to smallest.
\(2 > 1 > \frac{1}{2} > 0 > -\frac{1}{2}\)

Apply the exponent property to compare the expressions.
\(x^2 < x^1 < x^{\frac{1}{2}} < x^0 < x^{-\frac{1}{2}}\)

Answer A

Hope this helps!
ʕ•ᴥ•ʔ

If 0 < x < 1, which of the following is the greatest?

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GMAT Problem Solving (PS) Questions

If 0 < x < 1, which of the following is the greatest?

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