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Founder  Joined: 18 Apr 2015
Posts: 7419
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Kudos [?]: 1455 , given: 6625

Expert's post 00:00

Question Stats: 80% (01:24) correct 19% (00:55) wrong based on 56 sessions

 Quantity A Quantity B $$\frac{6^85^34^2}{3^68^2}$$ $$\frac{6^95^34^3}{3^82^8}$$

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.
[Reveal] Spoiler: OA

_________________ Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 363  , given: 66

1
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If we compare the two quantities we see we can simplify them until we get 1/64 and 1/96 so that A is larger! Manager Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 116  , given: 22

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We just compare the two values and try to simplify them.
A ------------------------------------------------B
6^8 * 5^3 * 4^2 / 3^6 * 8^2 ------------------ 6^9 * 5^3 * 4^3 / 3^8 * 2^8
Multiply them by the minimum power of each element in the two values. 3^6 /6^8 * 5^3 * 4^2
The result will be a simple form
1/ 8^2 -------------------------------------------6 * 4 /3^2 * 2^8

We convert 8^2 and 2^ 8 to one single form. 8^2 = (2^3)^2 = 2^2*3 = 2^ 6
1/ 2^6--------------------------------------------6* 4 / 2^ 8 *3^2
Multiply both is 2^6:
1-------------------------------------------------6 * 4 / 2^2 * 3^2 = 2/3
So B is bigger than A.
[/b]
_________________ Intern Joined: 20 Mar 2018
Posts: 34
GRE 1: Q164 V150 Followers: 1

Kudos [?]: 25  , given: 5

1
KUDOS
Instead of simplifying the whole terms, we can remove the terms which are common in both of the quantities and then compare the remaining parts
Manager Joined: 03 Apr 2019
Posts: 70
Followers: 0

Kudos [?]: 41 , given: 1

Let us remove the terms that are common on both sides
A: 1/8^2
B: (6*4)/(3^2 2^8 )
Lets rewrite A and B in terms of 2 and 3
A: 1/2^6
B: (2*3*2^2)/(3^2 2^8 )
Lets simplify the QTY B
A: 1/2^6
B: 2/3
Hence B is bigger. Re: 6^85^34^2/3^68^2   [#permalink] 05 Jul 2019, 02:03
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