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If p is a positive integer and p^3 is divisible by 144, then the large
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17 Aug 2021, 02:54
17 Aug 2021, 02:54
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63% (01:19) correct
36% (01:23) wrong based on 41 sessions
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If p is a positive integer and \(p^3\) is divisible by 144, then the largest positive integer that must divide p is
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Kudos for the right answer and explanation
Question part of the project GRE Quant/Math Extreme Challenge Daily (2021) Edition
GRE - Math Book
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Re: If p is a positive integer and p^3 is divisible by 144, then the large
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17 Aug 2021, 08:56
17 Aug 2021, 08:56
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Carcass wrote:
If p is a positive integer and \(p^3\) is divisible by 144, then the largest positive integer that must divide p is
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
\(p^3\) must be a perfect cube
\(144 = (12)(12) = (2^2)(3)(2^2)(3) = (2^4)(3^2)\)
Now, if (p)(p)(p) is divisible by \((2^4)(3^2)\)
Then, the factors of p must have powers which are multiple of 3
i.e. the minimum value of (p)(p)(p) must be \((2^6)(3^3)\)
So, p = \((2^2)(3) = 12\)
Hence, option E
Re: If p is a positive integer and p^3 is divisible by 144, then the large
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07 Mar 2024, 04:32
07 Mar 2024, 04:32
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