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n is an integer greater than zero [#permalink]
Expert's post 00:00

Question Stats: 47% (00:51) correct 52% (00:40) wrong based on 130 sessions
n is an integer greater than zero

 Quantity A Quantity B The number of different prime factors of 9n The number of different prime factors of 8n

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

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Last edited by Carcass on 11 Jun 2018, 08:55, edited 1 time in total. Founder  Joined: 18 Apr 2015
Posts: 13371
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Kudos [?]: 3402  , given: 12227

Re: n is an integer greater than zero [#permalink]
2
KUDOS
Expert's post
Explanation

Working smart on this kind of question: we do have 9n vs 8n, which means you do have at least on 3 on one side and at least one 2 on the other side. But no more than this.

if you look at n and use for instance 3, then we do have 3 and 3; 2 and 3. Hence, B is bigger.

If you consider 2, we do have 3 and 2, and 2 on the other side. A is greater.

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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Intern Joined: 08 Apr 2018
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Kudos [?]: 16  , given: 15

Re: n is an integer greater than zero [#permalink]
1
KUDOS
Carcass wrote:
n is an integer greater than zero

 Quantity A Quantity B The number of different prime factors of 9n The number of different prime factors of 8n

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.

Hello @carcass, please can you put the ABCD option in some of the questions you post? There are several questions you have posted that do not have the correct option. Is your answer correct is not a valid option for a standardized test, please. Intern Joined: 21 Nov 2017
Posts: 33
Followers: 0

Kudos [?]: 17  , given: 0

Re: n is an integer greater than zero [#permalink]
1
KUDOS
n > o, integer
. n = 1 --> 9n = 9 = 3^2 --> Quantity A = 1
8n = 8 = 2^3 --> Quantity B = 1
--> A = B
. n = 2 --> 9n = 9*2 = 3^2*2 --> Quantity A = 2
8n = 8*2 = 2^4 --> Quantity B = 1
--> A > B

Key: D GRE Instructor Joined: 10 Apr 2015
Posts: 3838
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Kudos [?]: 4499  , given: 69

Re: n is an integer greater than zero [#permalink]
4
KUDOS
Expert's post
Carcass wrote:
n is an integer greater than zero

 Quantity A Quantity B The number of different prime factors of 9n The number of different prime factors of 8n

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.

9n = (3)(3)(n)
8n = (2)(2)(2)(n)

We can see that, if n = 3, we get:
9n = (3)(3)(3)
8n = (2)(2)(2)(3)
In this case, 9n has ONE prime factor, and 8n has TWO prime factors
In other words, Quantity B is greater

Conversely, if n = 2, we get:
9n = (3)(3)(2)
8n = (2)(2)(2)(2)
In this case, 9n has TWO prime factors, and 8n has ONE prime factor
In other words, Quantity A is greater

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Intern Joined: 20 Feb 2020
Posts: 5
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Kudos [?]: 1 , given: 6

Re: n is an integer greater than zero [#permalink]
GreenlightTestPrep wrote:
Carcass wrote:
n is an integer greater than zero

 Quantity A Quantity B The number of different prime factors of 9n The number of different prime factors of 8n

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.

9n = (3)(3)(n)
8n = (2)(2)(2)(n)

We can see that, if n = 3, we get:
9n = (3)(3)(3)
8n = (2)(2)(2)(3)
In this case, 9n has ONE prime factor, and 8n has TWO prime factors
In other words, Quantity B is greater

Conversely, if n = 2, we get:
9n = (3)(3)(2)
8n = (2)(2)(2)(2)
In this case, 9n has TWO prime factors, and 8n has ONE prime factor
In other words, Quantity A is greater

Cheers,
Brent

Thanks for the explanation. It doesn't say the number of DISTINCT prime factors, should we assume that ourselves ?
Founder  Joined: 18 Apr 2015
Posts: 13371
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Kudos [?]: 3402 , given: 12227

Re: n is an integer greater than zero [#permalink]
Expert's post
Here we do have 9n and 8n BUT the n is common to taste both cases.

I.E. if n is 2 you have to use n=2 for both quantities.

You have to do that in order to compare and to assess which quantity is greater.

Two different prime numbers such as use n=2 and n=3 and to use 2 in the first quantity and 3 in the second has clearly no sense.

Regards
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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Re: n is an integer greater than zero   [#permalink] 29 Feb 2020, 12:21
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