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Intern
Joined: 12 May 2023
Posts: 20
Given Kudos: 65
GRE 1: Q154 V154
QCQ: The positive integer C has a prime
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Updated on: 24 Dec 2023, 18:00
Updated on: 24 Dec 2023, 18:00
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Question Stats:
62% (02:46) correct
37% (02:25) wrong based on 8 sessions
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The positive integer “C” has a prime factor that is not a factor of 60, and \(\frac{C}{450}\) is a prime number less than 100
Options:
A) Quantity A is Bigger
B) Quantity B is Bigger
C) The two quantities are equal
D) The relationship cannot be determined from the given information
Quantity A |
Quantity B |
C |
3000 |
Options:
A) Quantity A is Bigger
B) Quantity B is Bigger
C) The two quantities are equal
D) The relationship cannot be determined from the given information
Originally posted by LamoBear02 on 19 Sep 2023, 02:15.
Last edited by Carcass on 24 Dec 2023, 18:00, edited 1 time in total.
Last edited by Carcass on 24 Dec 2023, 18:00, edited 1 time in total.
Formatted
Re: QCQ: The positive integer C has a prime
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24 Dec 2023, 11:55
24 Dec 2023, 11:55
how does one approach this??
QCQ: The positive integer C has a prime
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25 Dec 2023, 01:00
25 Dec 2023, 01:00
Expert Reply
the prime factors of 60 are \(= 2^2*5*3\)
The prime factors of 450 are \(= 2*5^2*3^2\)
We do know that C to be divisible by 450 and has the same prime factors of 60 + some other factor
if we combine just the information above we do know that C is at least composed by the following factors
\(2^3*3^3*5^3 = 9000\)
\(\frac{9000}{450}\) must be a prime < 100
\(\frac{9000}{450 }=20\) and we do know that C is a prime < 100 and has also some other factor that 60 does not have.
Therefore our prime is at least 23 and C results to be > 9000
A is the answer
The prime factors of 450 are \(= 2*5^2*3^2\)
We do know that C to be divisible by 450 and has the same prime factors of 60 + some other factor
if we combine just the information above we do know that C is at least composed by the following factors
\(2^3*3^3*5^3 = 9000\)
\(\frac{9000}{450}\) must be a prime < 100
\(\frac{9000}{450 }=20\) and we do know that C is a prime < 100 and has also some other factor that 60 does not have.
Therefore our prime is at least 23 and C results to be > 9000
A is the answer
