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# If Q is a perfect square of an odd positive integer and if 8Q^8 has fo

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Joined: 05 Jan 2017
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If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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Updated on: 26 Jun 2017, 04:19
1
7
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:19) correct 45% (01:18) wrong based on 130 sessions

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If Q is a perfect 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

Originally posted by _shashank_shekhar_ on 26 Jun 2017, 04:00.
Last edited by Bunuel on 26 Jun 2017, 04:19, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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26 Jun 2017, 04:05
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The answer should be 3 as 8Q^8 will also have 2 as a factor since Q is odd. And since it's a perfect square, it's square root will have the same number of factors.

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Re: If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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26 Jun 2017, 06:32
1
Given Data
Q is a perfect square, and odd.
Also, given $$8Q^8$$ has 4 prime factors(of which 2 is a prime factor)

The expression $$8Q^8$$ has 3 more prime factors with the exception of 2.
Hence, √Q will also have 3 prime factors, since Q is a perfect square. (Option C)
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Re: If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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27 Jun 2017, 01:05
Thanks Guys, I understood where I was making a mistake.
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Re: If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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28 Jun 2017, 17:04
_shashank_shekhar_ wrote:
If Q is a perfect 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

We are given that Q is a perfect square of an odd positive integer. We know that the number of distinct prime factors of a number is the same as that number raised to any positive integer power. Since 8Q^8 has four distinct prime factors and 8 has one distinct prime factor (2), Q^8, or Q, must have three distinct prime factors. Since Q is a perfect square, √Q is also a positive integer. Lastly, since Q has three distinct prime factors, √Q has three distinct prime factors.

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If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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07 Jul 2017, 05:32
1
_shashank_shekhar_ wrote:
If Q is a perfect 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

Given Q is a perfect square of an odd positive integer.

Given $$8Q^8$$ has four prime factors.

8 has one prime factor, ie; 2.

Hence the other 3 prime factors must be from $$Q^8$$.

Therefore $$\sqrt{Q}$$ will also have 3 prime factors as its a perfect square.

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Re: If Q is a perfect square of an odd positive integer and if 8Q^8 has fo  [#permalink]

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19 Aug 2018, 08:40
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Re: If Q is a perfect square of an odd positive integer and if 8Q^8 has fo &nbs [#permalink] 19 Aug 2018, 08:40
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