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The sum of distinct prime factors

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Carcass
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The sum of distinct prime factors [#permalink] New post   Updated on: 11 Jun 2022, 22:29
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Quantity A
Quantity B
The sum of distinct prime factors of \(12^2\)
The sum of distinct prime factors of \(50^3 \)



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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Official Answer
B

Originally posted by Carcass on 06 May 2022, 03:53.
Last edited by Carcass on 11 Jun 2022, 22:29, edited 1 time in total.
Fixed OA
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GreenlightTestPrep
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Re: The sum of distinct prime factors [#permalink] New post   06 May 2022, 06:19
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Carcass wrote:
Quantity A
Quantity B
The sum of distinct prime factors of \(12^2\)
The sum of distinct prime factors of \(50^3 \)




\(12 = (2)(2)(3)\), which means \(12^2 = [(2)(2)(3)][(2)(2)(3)]\)
So, the sum of the distinct prime factors \(= 2 + 3 = 5\)

\(50 = (2)(5)(5)\), which means \(50^3 = [(2)(5)(5)][(2)(5)(5)][(2)(5)(5)]\)
So, the sum of the distinct prime factors \(= 2 + 5 = 7\)

Answer: B
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Re: The sum of distinct prime factors [#permalink] New post   11 Jun 2022, 11:50
GreenlightTestPrep wrote:
Carcass wrote:
Quantity A
Quantity B
The sum of distinct prime factors of \(12^2\)
The sum of distinct prime factors of \(50^3 \)




\(12 = (2)(2)(3)\), which means \(12^2 = [(2)(2)(3)][(2)(2)(3)]\)
So, the sum of the distinct prime factors \(= 2 + 3 = 5\)

\(50 = (2)(5)(5)\), which means \(50^3 = [(2)(5)(5)][(2)(5)(5)][(2)(5)(5)]\)
So, the sum of the distinct prime factors \(= 2 + 5 = 7\)

Answer: B


This was my answer as well, however the the correct answer appears as "C"

Carcass, care to share the explanation on this one? Thanks
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Re: The sum of distinct prime factors [#permalink] New post   11 Jun 2022, 12:35
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Create a factor tree to help visualize the factors of 12^2 and 50^3

The only distinct prime factors of 123 are 3 and 2. The only distinct prime factors of 503 are 5 and 2. Since they both have 2distinct prime factors, the quantities are equal.
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Re: The sum of distinct prime factors [#permalink] New post   11 Jun 2022, 14:03
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Carcass wrote:
OE

Create a factor tree to help visualize the factors of 12^2 and 50^3

The only distinct prime factors of 123 are 3 and 2. The only distinct prime factors of 503 are 5 and 2. Since they both have 2distinct prime factors, the quantities are equal.


I think the answer by GreenlightTestPrep is the correct answer.

The questions asked for the sum of distinct prime factors and NOT the number of distinct prime factors.

I think the question was not worded correctly for the intended answer!
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Re: The sum of distinct prime factors [#permalink] New post   11 Jun 2022, 16:01
2
Carcass wrote:
OE

Create a factor tree to help visualize the factors of 12^2 and 50^3

The only distinct prime factors of 123 are 3 and 2. The only distinct prime factors of 503 are 5 and 2. Since they both have 2distinct prime factors, the quantities are equal.


As alsafaj has noted, the question asks for the sum of distinct prime factors, not the number

3 + 2 < 5 + 2

Answer: B

I have changed the official answer to B.
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Re: The sum of distinct prime factors [#permalink] New post   16 Aug 2023, 02:47
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