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p is a prime number greater than 2.

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Carcass
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p is a prime number greater than 2. [#permalink] New post   31 Aug 2020, 10:17
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p is a prime number greater than 2.

Quantity A
Quantity B
The number of distinct prime factors of 27p
The number of distinct prime factors of 49p



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.
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Re: p is a prime number greater than 2. [#permalink] New post   31 Aug 2020, 10:17
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p is a prime number greater than 2. [#permalink] New post   31 Aug 2020, 14:15
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Carcass wrote:
p is a prime number greater than 2.

Quantity A
Quantity B
The number of distinct prime factors of 27p
The number of distinct prime factors of 49p



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.


First recognize that 27 = (3)(3)(3)
And 49 = (7)(7)

Let's test some possible values of p

case i: If p = 5, we get:
Quantity A: 27p = (3)(3)(3)(5). So, 27p has 2 distinct prime factors (3 and 5)
Quantity B: 49p = (7)(7)(5). So, 49p has 2 distinct prime factors (7 and 5)
In this case, Quantity A = Quantity B

case ii: If p = 7, we get:
Quantity A: 27p = (3)(3)(3)(7). So, 27p has 2 distinct prime factors (3 and 7)
Quantity B: 49p = (7)(7)(7). So, 49p has 1 distinct prime factor (7)
In this case, Quantity A is greater

Answer: D


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Re: p is a prime number greater than 2. [#permalink] New post   13 Sep 2020, 07:52
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Let,
p=3
quant A:3*27
no of distinct prime factors will be 1(that is 3)
quant B:3*49
no of distinct prime factors will be 2(that is 3,7)
quant A < quant B

p=5
quant A:5*27
no of distinct prime factors will be 2(that is 3,5)
quant B:5*49
no of distinct prime factors will be 2(that is 5,7)
quant A = quant B

so we can't determine the relationship answer D is correct
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Re: p is a prime number greater than 2. [#permalink] New post   21 May 2022, 02:43
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Just try to prove answer D. This is possible by choosing p = 3, and p = 7 for this question. No need to check for an additional p = 5, saving us extra few seconds.
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Re: p is a prime number greater than 2. [#permalink] New post   04 Sep 2024, 15:39
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: p is a prime number greater than 2. [#permalink]
04 Sep 2024, 15:39
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