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Math Expert V
Joined: 02 Sep 2009
Posts: 57244
If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 81% (00:53) correct 19% (01:05) wrong based on 135 sessions

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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

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Originally posted by Bunuel on 13 Jun 2017, 08:50.
Last edited by SajjadAhmad on 03 Jul 2019, 04:56, edited 1 time in total.
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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1
Bunuel wrote:
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

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...
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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1
Bunuel wrote:
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

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

Answer option E
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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Bunuel wrote:
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

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)
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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Bunuel wrote:
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

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.
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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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
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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1
Bunuel wrote:
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

0<k<1...

A.) 3k/2 > k

B.) 1/k > k

C.) |k| = k

D.) $$\sqrt{k}$$ > k

E.) k^2 < k

Answer E.

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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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1
Bunuel wrote:
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

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
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Re: If 0 < k < 1, then which of the following must be less than k?  [#permalink]

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_________________ Re: If 0 < k < 1, then which of the following must be less than k?   [#permalink] 15 Aug 2018, 05:45
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# If 0 < k < 1, then which of the following must be less than k?

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