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n is an integer greater than zero

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n is an integer greater than zero [#permalink] New post 27 Nov 2017, 12:13
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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.
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Re: n is an integer greater than zero [#permalink] New post 27 Nov 2017, 12:24
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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.

D is the answer
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Re: n is an integer greater than zero [#permalink] New post 10 Jun 2018, 19:19
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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.
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Re: n is an integer greater than zero [#permalink] New post 13 Jun 2018, 18:23
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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
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Re: n is an integer greater than zero [#permalink] New post 23 May 2019, 08:16
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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

Answer: D

Cheers,
Brent
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Re: n is an integer greater than zero [#permalink] New post 29 Feb 2020, 12:02
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

Answer: D

Cheers,
Brent


Thanks for the explanation. It doesn't say the number of DISTINCT prime factors, should we assume that ourselves ?
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Re: n is an integer greater than zero [#permalink] New post 29 Feb 2020, 12:21
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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.


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Re: n is an integer greater than zero   [#permalink] 29 Feb 2020, 12:21
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