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# a > 1 and b > 5

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Moderator
Joined: 18 Apr 2015
Posts: 5130
Followers: 77

Kudos [?]: 1029 [0], given: 4636

a > 1 and b > 5 [#permalink]  18 Jul 2018, 11:25
Expert's post
00:00

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.

Kudos for R.A.E
[Reveal] Spoiler: OA

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Director
Joined: 07 Jan 2018
Posts: 553
Followers: 4

Kudos [?]: 477 [1] , given: 84

Re: a > 1 and b > 5 [#permalink]  19 Jul 2018, 01:35
1
KUDOS
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
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: a > 1 and b > 5   [#permalink] 19 Jul 2018, 01:35
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