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10 Feb 2023, 15:16
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:16) correct
44%
(02:24)
wrong
based on 130
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Not Attempted Yet
If a and b are positive, is \(a^{\frac{b}{2}} > a^{2b}\) ?
(1) \(1 < b < b^a\)
(2) \(a < b\)
(1) \(1 < b < b^a\)
(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
12 Feb 2023, 09:46
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Bunuel
\(a^{\frac{b}{2}} > a^{2b}\)
As its given that a and b are positive, \(\frac{b }{ 2}\) will always be lesser than 2b
Now, \(a^{\text {smaller +ve value}} > a^{\text {larger +ve value}}\) when a is between 0 and 1
\(a^{\text {smaller +ve value}} < a^{\text {larger +ve value}}\) when a is greater than 1
In a nutshell, we want to find whether a lies between 0 and 1
Let's start with Statement II
(2) \(a < b\)
We know a is less than b, however we don't know the interval a lies. Hence, the statement is not sufficient and we can eliminate B and D.
Statement I
(1) \(1 < b < b^a\)
As \(b > 1, b < b^a\) that essentially tells us that a > 1
hence, the statement is sufficient.
Option A
15 Feb 2023, 23:01
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Bunuel
The stem can be simplified to is \(\sqrt {a^b}> (a^b)^2\)
This is only possible if \(a^b\) in the range between \(0\) and \(1\), so \(a\) has to be \(a < 1 \)
(1) \(1 < b < b^a\)
This is only possible if \(a >1\).
We can answer NO to the stem.
SUFF.
(2) \(a < b\)
\(a= \frac{1}{2}\), \(b = 2\) Yes to the stem
\(a= 2, b =4 \) No to the stem.
INSUFF.
Ans A
Hope it's clear.
