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11 Sep 2023, 05:00
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B
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Difficulty:
85%
(hard)
Question Stats:
33% (02:10) correct
68%
(01:27)
wrong
based on 40
sessions
History
Date
Time
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Not Attempted Yet
If a^2 = b, is 1 > a > 0?
(1) 1 > b > 0
(2) a > b
(1) 1 > b > 0
(2) a > b
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
Updated on: 11 Sep 2023, 22:18
Originally posted by BrushMyQuant on 11 Sep 2023, 05:38.
Last edited by BrushMyQuant on 11 Sep 2023, 22:18, edited 2 times in total.
Last edited by BrushMyQuant on 11 Sep 2023, 22:18, edited 2 times in total.
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Given that a^2 = b and we need to find if 1 > a > 0
1 > a > 0 => 0 < a < 1
STAT 1: 1 > b > 0
=> 0 < b < 1
=> 0 < \(a^2\) < 1
=> -1 < a < 0 and 0 < a < 1
NOT SUFFICIENT as a can be between -1 and 0 also
STAT 2: a > b
a^2 = b
=> b is non-negative
and a > b
=> both a and b cannot be zero and are positive
a^2 = b
=> a = ±\(\sqrt{b}\)
But a is positive
=> a = \(\sqrt{b}\)
Now, a > b
=> \(\sqrt{b}\) > b
This is true only when b is a fraction, positive fraction in this case, between 0 and 1
Ex: b = 0.01
=> \(\sqrt{b}\) = \(\sqrt{0.01}\) = 0.1
=> \(\sqrt{b}\) > b (i.e. 0.1 > 0.01)
Since, b is a positive fraction between 0 and 1
=> b^2 is also a positive fraction between 0 and 1
=> 0 < a < 1
=> SUFFICIENT
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Inequalities
1 > a > 0 => 0 < a < 1
STAT 1: 1 > b > 0
=> 0 < b < 1
=> 0 < \(a^2\) < 1
=> -1 < a < 0 and 0 < a < 1
NOT SUFFICIENT as a can be between -1 and 0 also
STAT 2: a > b
a^2 = b
=> b is non-negative
and a > b
=> both a and b cannot be zero and are positive
a^2 = b
=> a = ±\(\sqrt{b}\)
But a is positive
=> a = \(\sqrt{b}\)
Now, a > b
=> \(\sqrt{b}\) > b
This is true only when b is a fraction, positive fraction in this case, between 0 and 1
Ex: b = 0.01
=> \(\sqrt{b}\) = \(\sqrt{0.01}\) = 0.1
=> \(\sqrt{b}\) > b (i.e. 0.1 > 0.01)
Since, b is a positive fraction between 0 and 1
=> b^2 is also a positive fraction between 0 and 1
=> 0 < a < 1
=> SUFFICIENT
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Inequalities
11 Sep 2023, 11:50
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BrushMyQuant
Hello BMQ
I hope you're well.
Option B provides sufficient information.
Its given that a^2 = b
So, b will always be equal to or greater than 0 (non-negative).
a=\sqrt{ b}
(A) is insufficient.
(B) states that a>b
so, b and a cannot be 0. They both are positive.
and a=\sqrt{b}
Root of a number is greater than the number only when the number is between 0 and 1 (I am keeping in view the non-negative part from the question stem).
Option B allows us to place a between 0 and 1.
Let me know in case I am missing something here.
Thank you.
