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If Q the square of an odd positive integer and if 8Q^8 has four prime

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If Q the square of an odd positive integer and if 8Q^8 has four prime  [#permalink]

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New post 25 Nov 2019, 01:20
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If Q the square of an odd positive integer and if 8Q^8 has four prime factors, then how many prime factors does √Q have?

A. 1
B. 2
C. 3
D. 4
E. Cannot be determined

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Re: If Q the square of an odd positive integer and if 8Q^8 has four prime  [#permalink]

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New post 25 Nov 2019, 03:41
As \(Q^2\) is an odd number, \(Q^8\) must be odd too.

\(2^3*Q^8\) has 4 prime factors; hence, \(Q^8\) must have 3 prime factors, and so does \(\sqrt{Q}\).

Bunuel wrote:
If Q the square of an odd positive integer and if 8Q^8 has four prime factors, then how many prime factors does √Q have?

A. 1
B. 2
C. 3
D. 4
E. Cannot be determined

Are You Up For the Challenge: 700 Level Questions
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If Q the square of an odd positive integer and if 8Q^8 has four prime  [#permalink]

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New post 26 Nov 2019, 06:29
Bunuel wrote:
If Q the square of an odd positive integer and if 8Q^8 has four prime factors, then how many prime factors does √Q have?

A. 1
B. 2
C. 3
D. 4
E. Cannot be determined

Are You Up For the Challenge: 700 Level Questions

Q=(2n+1)^2
Q^8=(2n+1)^16
\(8*Q^8= 2^3*(2n+1)^(16)\)
This means 2n+1 consists of 3 prime factors as 2 is one prime factor and total prime factors in 8Q^8 is 4
So \(\sqrt{Q}\) has 3 prime factors.
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If Q the square of an odd positive integer and if 8Q^8 has four prime   [#permalink] 26 Nov 2019, 06:29
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If Q the square of an odd positive integer and if 8Q^8 has four prime

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