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

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

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New post 19 Oct 2018, 12:00
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A
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C
D
E

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

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New post 19 Oct 2018, 12:10
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1
SajjadAhmad wrote:
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.

Answer choice E

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

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New post 14 Apr 2020, 02:46
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@experts is there a shorter way to do such questions? it takes a lot of time in trial and error.
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Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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New post 31 May 2020, 04:42
Bumping it again. Is there any shorter way to do it apart from hit and trial?
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Re: If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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New post 31 May 2020, 23:38
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
Please give Kudos if you found this Helpful.
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If a^1/2 > b > c^2, which of the following could be true?  [#permalink]

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New post 01 Jun 2020, 00:10
1
\(\sqrt{a}\) > 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




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

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New post 02 Jun 2020, 22:40
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
Please give Kudos if you found this Helpful.


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

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New post 03 Jun 2020, 06:13
1
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
Please give Kudos if you found this Helpful.


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

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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?

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