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TAGS: Founder  Joined: 18 Apr 2015
Posts: 6920
Followers: 114

Kudos [?]: 1344  , given: 6318

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Expert's post 00:00

Question Stats: 61% (00:33) correct 38% (00:37) wrong based on 34 sessions
 Quantity A Quantity B $$\frac{{99}^{9}}{{9^{99}}}$$ $$\frac{{11}^{9}}{{9}^{90}}$$

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

_________________ Manager Joined: 28 Nov 2017
Posts: 54
Followers: 1

Kudos [?]: 39  , given: 32

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A very Smart Question Rather :

To solve or Compare the two Quantities we will try to get the Fraction ( In particular the Denominator Same for both Qty )

For Qty A we have the Following Situation :

99^ 9 / 9 ^ 99 = ( 11 * 9 ) ^ 9 / 9 ^99 --> 9^9(11^9)/ 9 ^ 99 --> 11^9 / 9 ^ 90 [ We divided or Took 9^ 9 out as Common ] .

So Both Qty are equal GRE Instructor Joined: 10 Apr 2015
Posts: 1991
Followers: 60

Kudos [?]: 1806  , given: 9

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Expert's post
Carcass wrote:
 Quantity A Quantity B $$\frac{{99}^{9}}{{9^{99}}}$$ $$\frac{{11}^{9}}{{9}^{90}}$$

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

Key Concept: $$(b^k)(c^k)=(bc)^k$$

We can also write: $$(bc)^k=(b^k)(c^k)$$

Notice that we can rewrite 99 as (9)(11)
So....

GIVEN:
QUANTITY A: $$\frac{99^9}{9^{99}}$$

QUANTITY B: $$\frac{11^9}{9^{90}}$$

Rewrite 99 as (9)(11) to get:
QUANTITY A: $$\frac{[(9)(11)]^9}{9^{99}}=\frac{(9^9)(11^9)}{9^{99}}=\frac{11^9}{9^{90}}$$

QUANTITY B: $$\frac{11^9}{9^{90}}$$

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: 99^9/9^99 or 11^9/9^90   [#permalink] 08 Jun 2019, 08:06
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