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# If a^2 = b, is 1 > a > 0?

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
If a^2 = b, is 1 > a > 0?  [#permalink]

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29 Jul 2015, 02:11
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Difficulty:

95% (hard)

Question Stats:

39% (01:53) correct 61% (01:49) wrong based on 159 sessions

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If a^2 = b, is 1 > a > 0?

(1) 1 > b > 0
(2) a > b

Kudos for a correct solution.

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Joined: 14 Mar 2014
Posts: 146
GMAT 1: 710 Q50 V34
Re: If a^2 = b, is 1 > a > 0?  [#permalink]

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29 Jul 2015, 02:46
Bunuel wrote:
If a^2 = b, is 1 > a > 0?

(1) 1 > b > 0
(2) a > b

Kudos for a correct solution.

IMO : B

Statement 1: 0< b< 1

if b lies in 0< b< 1 then
a can lie in 0< a< 1 or -1 < a< 0.
For eg: if b = 1/4 then a can be 1/2 or -1/2 .
Not suff

Statement 2: a > b
Given $$a^2 = b$$ i.e b >=0. And if a>b then a must also be >=0
If a>b then
for a>1 then $$a^2 > b$$. They cannot be equal
so a must be in interval 0<a<1

PS: a cannot be equal to "0" or "1" since it violates the statement 2: a>b
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Re: If a^2 = b, is 1 > a > 0?  [#permalink]

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29 Jul 2015, 02:50
2
Bunuel wrote:
If a^2 = b, is 1 > a > 0?

(1) 1 > b > 0
(2) a > b

Kudos for a correct solution.

Statement 1:
If 1>b>0 and a^2 = b, >>> A must be a fraction e.g. 1/2^2 = 1/4 or -1/2^2=1/4. Resulting in Yes/No for the question above. IS.

Statement 2:
a > b tells us that, a is positive since a^2 = b (which must be positive). Therefore a must be a positive fraction e.g. 1/2, 3/4 ...

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Posts: 52906
Re: If a^2 = b, is 1 > a > 0?  [#permalink]

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17 Aug 2015, 08:31
Bunuel wrote:
If a^2 = b, is 1 > a > 0?

(1) 1 > b > 0
(2) a > b

Kudos for a correct solution.

800score Official Solution:

Statement (1) tells us that b is between 0 and 1, so we also know that a² is between 0 and 1 since b = a². If a is any number between -1 and 1, then a² will be
between 0 and 1, so Statement (1) is insufficient.

Statement (2) tells us that a > b, and since a² = b, we know that a > a². This is only true for
numbers between 0 and 1. The square of any number that is larger than 1 or negative will be larger than the number itself. So Statement (2) is sufficient.

Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).
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Re: If a^2 = b, is 1 > a > 0?  [#permalink]

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12 Feb 2019, 14:07
I did it differently... Don't know if I'm right.

I restated the question first.

a^2=b (1)

1>a>0 It is the same as 0<a<1.

The inequality that can result in a range like that is:

a*(a-1)<0

So now we have:

a^2-a<0 , as we already know from (1), a^2=b so,

b-a<0
b<a

So our question is is a>b?

The only clear statement that gives us information about a & b is statement (2). So B is the answer.
Re: If a^2 = b, is 1 > a > 0?   [#permalink] 12 Feb 2019, 14:07
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