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GMAT Club team member V
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If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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12 00:00

Difficulty:   95% (hard)

Question Stats: 39% (02:14) correct 61% (01:59) wrong based on 132 sessions

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If $$\sqrt{a}$$ > b > $$c^2$$, 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

Source: Experts Global GMAT

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Posts: 504
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Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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1
If $$\sqrt{a}$$ > b > $$c^2$$, 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

EG

let a = 9
b = 2
c = 1

Then 9 > 2 > 1 and this maintains the question stem condition.

3 > 2 > 1

c = 1/2
b = 1/3
a = 1/4

1/2 > 1/3 > 1/4 this the second case.

Sqrt of 1/4 = 1/2

1/2 > 1/3 > 1/4 is possible.

Now last case

a > c > b

a = 1/4
c = 1/6
b = 1/8

1/2 > 1/8 > 1/36 possible.

All the cases are possible.

Posted from my mobile device
Director  P
Joined: 21 Feb 2017
Posts: 618
Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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@experts is there a shorter way to do such questions? it takes a lot of time in trial and error.
Manager  G
Joined: 05 May 2019
Posts: 148
Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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Bumping it again. Is there any shorter way to do it apart from hit and trial?
Manager  S
Joined: 10 Oct 2017
Posts: 80
Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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ajaygaur319 wrote:
Bumping it again. Is there any shorter way to do it apart from hit and trial?

Kritisood ajaygaur319

Whenever you see \sqrt{a}, you can consider the value as .404
for .404 \sqrt{a}>a>a^2.

For each option consider the values of a, b, c as .404, . 405 and .406 or .404, .403, .402 depending on the option because \sqrt{.403}>.404.
That's the fastest way to tackle the Square root questions
DS Forum Moderator V
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Posts: 1980
Location: India
If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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$$\sqrt{a}$$ > b > $$c^2$$

First thing we can infer is a>0 ,b>=0, but c can be negative.

Hence I. a > b > c and III. a > c > b can be true without even checking. ( Take 'a' very large number(10000000). Now if you draw $$b=c^2$$, it get cuts twice in that range by b=c. Hence b>c or c>b can be possible in range (0<b<1)

If this can be true c > b > a , we must take +ve value of c and b as a can't be negative. Since $$c>b>c^2$$, c<1.

c=0.5; b=0.4; a=0.36

$$\sqrt{a} =0.6; b=0.4; c^2=0.25$$

E

If $$\sqrt{a}$$ > b > $$c^2$$, 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

Source: Experts Global GMAT
Director  P
Joined: 21 Feb 2017
Posts: 618
Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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naveenban wrote:
ajaygaur319 wrote:
Bumping it again. Is there any shorter way to do it apart from hit and trial?

Kritisood ajaygaur319

Whenever you see \sqrt{a}, you can consider the value as .404
for .404 \sqrt{a}>a>a^2.

For each option consider the values of a, b, c as .404, . 405 and .406 or .404, .403, .402 depending on the option because \sqrt{.403}>.404.
That's the fastest way to tackle the Square root questions

Im sorry, couldn't understand this approach. chetan2u GMATinsight any shortcuts for such questions? Would appreciate the help.
GMAT Club Legend  V
Status: GMATINSIGHT Tutor
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Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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Kritisood

The language says "which of the following could be true?"

In such question we have seek one example for which given expression is/are true

What we have is $$\sqrt{a}$$ > b > $$c^2$$

So first example, c = 1, b = 2, a = 9 i.e. a > b > c Also $$√9 > 2 > (1)^2$$ I part true

So Second example, keeping in mind II. c > b > a , Since a myst be smaller than b while √a should be greater so it's possible only for values between 0 and 1

we can take, c = 1/2, b = 1/3, a = 1/4 i.e. c > b > a because $$√1/4 > 1/3 > (1/2)^2$$ II part true

III. a > c > b, This is easy, we can take a = 1, c = 1/2 and b= 1/3 because $$√1 > 1/3 > (1/2)^2$$ III part true

Quote:
If $$\sqrt{a}$$ > b > $$c^2$$, 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

Kritisood wrote:
naveenban wrote:
ajaygaur319 wrote:
Bumping it again. Is there any shorter way to do it apart from hit and trial?

Kritisood ajaygaur319

Whenever you see \sqrt{a}, you can consider the value as .404
for .404 \sqrt{a}>a>a^2.

For each option consider the values of a, b, c as .404, . 405 and .406 or .404, .403, .402 depending on the option because \sqrt{.403}>.404.
That's the fastest way to tackle the Square root questions

Im sorry, couldn't understand this approach. chetan2u GMATinsight any shortcuts for such questions? Would appreciate the help.

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FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol. Re: If a^1/2 > b > c^2, which of the following could be true?   [#permalink] 03 Jun 2020, 06:13

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