GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 27 Jun 2019, 03:26 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If n is an integer and n^4 is divisible by 32, which of the

Author Message
TAGS:

Hide Tags

VP  D
Joined: 09 Mar 2016
Posts: 1274
If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

Show Tags

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!
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3364
Location: India
GPA: 3.12
Re: If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

Show Tags

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.

_________________
You've got what it takes, but it will take everything you've got
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3364
Location: India
GPA: 3.12
If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

Show Tags

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
Intern  B
Joined: 28 Aug 2018
Posts: 27
Location: India
Schools: LBS '21 (A)
GMAT 1: 650 Q49 V31 GPA: 3.16
Re: If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

Show Tags

Simple observation works -
For n^4 to be divisible by 32 , n^4 must be in the form of 2^5*x. Where x is any other number. Out of all the choices only B) that has n = 4 suffices the condition of 2^5x. Rest all the answer choices will not yield 2^5x if their square are squared.
Manager  B
Joined: 12 Jul 2018
Posts: 65
Location: India
Schools: ISB '20, NUS '21
GMAT 1: 420 Q26 V13 GMAT 2: 540 Q44 V21 Re: If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

Show Tags

[quote=
Given: $$n^4=32k=2^5k$$ --> $$n=2\sqrt{2k}$$ --> as $$n$$ is an integer, the least value of $$n$$ is obtained when $$k=8$$ --> $$n_{min}=2\sqrt{2*8}=4$$ --> $$\frac{n_{min}}{32}=\frac{4}{32}$$ gives remainder of $$4$$.

quote]

how come 4/32 gives remainder as 4?
Shouldn't it be 8?
_________________
Please press +1 Kudos to support
Keep your eyes on the prize: 750
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: If n is an integer and n^4 is divisible by 32, which of the  [#permalink]

Show Tags

deddex wrote:
[quote=
Given: $$n^4=32k=2^5k$$ --> $$n=2\sqrt{2k}$$ --> as $$n$$ is an integer, the least value of $$n$$ is obtained when $$k=8$$ --> $$n_{min}=2\sqrt{2*8}=4$$ --> $$\frac{n_{min}}{32}=\frac{4}{32}$$ gives remainder of $$4$$.

Quote:

how come 4/32 gives remainder as 4?
Shouldn't it be 8?

Let me ask you a question: how many leftover apples would you have if you had 4 apples and wanted to distribute in 32 baskets evenly? Each basket would get 0 apples and 4 apples would be leftover (remainder).

When a divisor is more than dividend, then the remainder equals to the dividend, for example:
4 divided by 32 yields the reminder of 3: $$4=32*0+4$$;
3 divided by 4 yields the reminder of 3: $$3=4*0+3$$;
9 divided by 14 yields the reminder of 9: $$9=14*0+9$$;
1 divided by 9 yields the reminder of 1: $$1=9*0+1$$.

For more on this check:

5. Divisibility/Multiples/Factors

6. Remainders

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
_________________ Re: If n is an integer and n^4 is divisible by 32, which of the   [#permalink] 07 Dec 2018, 02:22

Go to page   Previous    1   2   [ 26 posts ]

Display posts from previous: Sort by

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