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If a^(1/2) > b^2 > c^4, which of the following could be true?

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If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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New post 19 Mar 2018, 11:04
2
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (01:53) correct 68% (02:13) wrong based on 41 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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Re: If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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New post 19 Mar 2018, 11:34
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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Re: If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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New post 19 Mar 2018, 11:42
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
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Re: If a^(1/2) > b^2 > c^4, which of the following could be true?  [#permalink]

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New post 19 Mar 2018, 11:46
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? &nbs [#permalink] 19 Mar 2018, 11:46
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