If 0

Question

If 0 < k < 1, then which of the following must be less than k?

(A) 3k/2

(B) 1/k

(C) |k|

(D)  \sqrt{k}

(E) k^2

Source:   Nova GMAT  
Difficulty Level:   500

sashiim20 · Accepted Answer

Let k =  \frac{1}{2}

(A)  \frac{3k}{2} = \frac{3}{2} * \frac{1}{2} = \frac{3}{4}  ------- Greater than k

(B)  \frac{1}{k} = \frac{1}{(1/2)}  = 2 ------------ Greater than k

(C) |k| =  \frac{1}{2}  ----------- Equal to k

(D)  \sqrt{k}  =  \sqrt{\frac{1}{2}}  = 0.707 ------------- Greater than k

(E)  k^2  =  (\frac{1}{2})^2  =  \frac{1}{4}  -------- Less than k 
Answer E...

GMATinsight · Answer

Higher powers result in a smaller number when the number is between 0 and 1

Answer option E

Abhishek009 · Answer

Let k = 0.50

(A)  \frac{3k}{2} = \frac{3*0.50}{2} = 0.75   ( Not Possible )

(B)  \frac{1}{k} = \frac{1}{0.50} = 2   ( Not Possible )

(C)  |k| = |0.50|   ( Not Possible )

(D)  \sqrt{k}  =  \sqrt{0.50}  =  0.70   ( Not Possible )

(E)  k^2 = 0.50^2 = 0.25   ( Possible )

Answer will hence be (E)

Shruti0805 · Answer

The question basically indicates that the value of k is a positive fraction. In such cases, the greater the value of denominator, the smaller the overall value of the fraction.
Out of all the options,  k^2  would increase the value of the denominator the most and thus E should be the correct answer.

RaguramanS · Answer

0<k<1
So k= proper fraction=1/2, 1/3, 1/4
Sub any of the above value in the options
Avoid decimals, as it may cause some confusions.

Option E alone will be less than k

shashankism · Answer

0 k B.) 1/k > k C.) |k| = k D.) \sqrt{k} > k E.) k^2 < k Answer E.

ScottTargetTestPrep · Answer

We are given that 0 < k < 1, so k is a positive proper fraction. We may recall that when a positive proper fraction is raised to an exponent greater than 1, it will result in a lesser value. Thus, k^2 < k.
 
Answer: E

bumpbot · Answer

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If 0 < k < 1, then which of the following must be less than k?

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GMAT Problem Solving (PS) Questions

If 0 < k < 1, then which of the following must be less than k?

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