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

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

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New post 29 Jul 2015, 03:11
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If a^2 = b, is 1 > a > 0?

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

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Spoiler: OA

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

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New post 29 Jul 2015, 03:46
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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New post 29 Jul 2015, 03:50
1
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 ...

Answer B.
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Re: If a^2 = b, is 1 > a > 0? [#permalink]

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New post 17 Aug 2015, 09:31
1
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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Re: If a^2 = b, is 1 > a > 0?   [#permalink] 15 Sep 2017, 00:33
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