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a > 1 and b > 5

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a > 1 and b > 5 [#permalink] New post 18 Jul 2018, 11:25
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Question Stats:

78% (00:40) correct 21% (00:02) wrong based on 14 sessions
\(a > 1\)

\(b > 5\)

Quantity A
Quantity B
\((5b)^a\)
\((b^2)^a\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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Re: a > 1 and b > 5 [#permalink] New post 19 Jul 2018, 01:35
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Let us expand both quantities.
Starting with qty A

\((5b)^a\) can be re-written as \(5^a * b^a\)

qty B is equal to
\(b^2^a\)

Let us divide both sides by \(b^a\); remember that \(b\) is positive so when be is raised to any power the result will be +ve.

qty A will equal
\(5^a\)
while qty B will equal
\(b^a\)

Since \(b > 5\) ; \(b^a\) will always be greater than \(5^a\) since a is also a +ve no greater than 1
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Re: a > 1 and b > 5   [#permalink] 19 Jul 2018, 01:35
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a > 1 and b > 5

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