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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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2 00:00

Difficulty:   95% (hard)

Question Stats: 37% (02:49) correct 63% (02:02) wrong based on 43 sessions

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If $$\sqrt{a} > b^2 > c^4$$, which of the following could be true?

I. a > b > c
II. c > b > a
III. a > c > b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III only

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Manager  S
Joined: 22 May 2017
Posts: 120
Re: If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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In case of +ve nos
I is true

Let us consider negative number
For b^2 and c^4
9>1
(-3)^2 > (-1)^4

But - 3 < - 1
SO b<c
Now a is under root it has to be +ve to be greater

IN CASE OF above
Eg sqrt 100 > 9 > 1
a = 100, b=-3, c= - 1
So a will be greater than b and c always

So I and III are true
Hence D

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Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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2
pushpitkc wrote:
If $$\sqrt{a} > b^2 > c^4$$, which of the following could be true?

I. a > b > c
II. c > b > a
III. a > c > b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III only

Statement 1: a=100, b=2 & c=1. $$\sqrt{a}=10$$, $$b^2=4$$ & $$c^4=1$$. Hence could be true

Statement 2: a=0.01, b=0.02, c=0.03, then $$\sqrt{a}=0.1$$, $$b^2=0.0004$$ & $$c^4=0.81*10^{-6}$$. Hence could be true

Statement 3: a=1, b=0.1 & c=0.2, then $$\sqrt{a}=1$$, $$b^2=0.01$$ & $$c^4=0004$$. Hence could be true

Option E
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1214
Location: India
GPA: 3.82
Re: If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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akshata19 wrote:
In case of +ve nos
I is true

Let us consider negative number
For b^2 and c^4
9>1
(-3)^2 > (-1)^4

But - 3 < - 1
SO b<c
Now a is under root it has to be +ve to be greater

IN CASE OF above
Eg sqrt 100 > 9 > 1
a = 100, b=-3, c= - 1
So a will be greater than b and c always

So I and III are true
Hence D

Posted from my mobile device

Hi akshata19

this is a could be true question, hence our objective is to find a combination that satisfies the statements while following the question stem. Hence testing negative numbers will negate the question stem which is not possible in this case Re: If a^(1/2) > b^2 > c^4, which of the following could be true?   [#permalink] 19 Mar 2018, 11:46
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# If a^(1/2) > b^2 > c^4, which of the following could be true?

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