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# If n is an integer and n^4 is divisible by 32, which of the

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Director
Joined: 09 Mar 2016
Posts: 951
If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

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25 Jul 2018, 02:48
thank you Bunuel one question why do you assume that least value is 8 ? whats your reasoning ? can you please explain
as $$n$$ is an integer, the least value of $$n$$ is obtained when $$k=8$$ -

And how did you figure out these values $$8$$ for $$k=2^3*2^4$$, $$12$$ for $$k=2^3*3^4$$

for instance this $$k=2^3*2^4$$, how should I understand it ? for example for n to be 4 k= 8 but you didn't break down this into exponents unlike other examples

hey pushpitkc, may be you can explain/answer the above questions thanks!
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Joined: 26 Feb 2016
Posts: 3199
Location: India
GPA: 3.12
Re: If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

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26 Jul 2018, 05:38
dave13 wrote:
thank you Bunuel one question why do you assume that least value is 8 ? whats your reasoning ? can you please explain
as $$n$$ is an integer, the least value of $$n$$ is obtained when $$k=8$$ -

And how did you figure out these values $$8$$ for $$k=2^3*2^4$$, $$12$$ for $$k=2^3*3^4$$

for instance this $$k=2^3*2^4$$, how should I understand it ? for example for n to be 4 k= 8 but you didn't break down this into exponents unlike other examples

hey pushpitkc, may be you can explain/answer the above questions thanks!

Hey dave13

Let me try and explain this question once again.

If $$n^4$$ is divisible by 32, we have been asked to find which of the answer
options can be the remainder when n is divided by 32.

The first step is to prime-factorize 32 which is $$2^5$$. n has to contain a
minimum of $$2^2$$ in order for $$n^4$$ to be divisible by $$32(2^5)$$.
If n had only one 2, then $$n^4$$ would contain $$2^4$$ and not be divisible by 32.

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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3199
Location: India
GPA: 3.12
If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

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26 Jul 2018, 05:39
1
dave13 wrote:
thank you Bunuel one question why do you assume that least value is 8 ? whats your reasoning ? can you please explain
as $$n$$ is an integer, the least value of $$n$$ is obtained when $$k=8$$ -

And how did you figure out these values $$8$$ for $$k=2^3*2^4$$, $$12$$ for $$k=2^3*3^4$$

for instance this $$k=2^3*2^4$$, how should I understand it ? for example for n to be 4 k= 8 but you didn't break down this into exponents unlike other examples

hey pushpitkc, may be you can explain/answer the above questions thanks!

Hey dave13

Let me try and explain this question once again.

If $$n^4$$ is divisible by 32, we have been asked to find a remainder(from answer options) when n is divided by 32.

First, we have to prime-factorize 32 which is $$2^5$$.

Now, n has to contain a minimum of $$2^2$$ in order for $$n^4$$ to be divisible by $$32(2^5)$$. In order to validate our answer,
we can test a smaller value - If n had only one 2, then $$n^4$$ would contain $$2^4$$ and that would not be divisible by 32.

_________________

You've got what it takes, but it will take everything you've got

If n is an integer and n^4 is divisible by 32, which of the &nbs [#permalink] 26 Jul 2018, 05:39

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