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

It is currently 21 Aug 2018, 01:31

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2650
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the  [#permalink]

Show Tags

New post Updated on: 25 Nov 2016, 07:39
4
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:08) correct 44% (01:10) wrong based on 100 sessions

HideShow timer Statistics


Originally posted by stonecold on 24 Nov 2016, 13:32.
Last edited by stonecold on 25 Nov 2016, 07:39, edited 2 times in total.
Renamed the topic and edited the question.
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1392
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the  [#permalink]

Show Tags

New post 24 Nov 2016, 19:39
3
stonecold wrote:
If \(p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3\),what will be the remainder when p is divided by 5?

A)zero
B)one
C)two
D)three
E)four


Solution 1:
To find the remainder when divide by 5, first we need to find the units digit.

\(1^3=1\) has units digit 1
\(3^3=27\) has units digit 7
\(5^3=125\) has units digit 5
\(7^3=343\) has units digit 3
\(9^3=729\) has units digit 9
\(11^3\) has units digit 1
\(13^3\) has the same units digit as \(3^3\), which has units digit 7

So the units digit of \(p\) is \(1+7+5+3+9+1+7=43\) or the units digit is 3.
So the remainder is 3 when divide \(p\) by 5.

Solution 2:
\(1^3 \equiv 1 \pmod{5}\)
\(3^3=(5-2)^3 \equiv -2^3 \pmod{5}\)
\(5^3 \equiv 0 \pmod{5}\)
\(7^3 =(5+2)^3 \equiv 2^3 \pmod{5}\)
\(9^3 =(5 \times 2-1)^3 \equiv -1^3 \pmod{5}\)
\(11^3 = (5 \times 2 +1)^3 \equiv 1^3 \pmod{5}\)
\(13^3 =(5 \times 3 -2)^3 \equiv -2^3 \pmod{5}\)

So \(p \equiv 1-2^3+0+2^3-1^3+1^3-2^3 \pmod{5}\)
\(\implies p \equiv 1-8=-7 \pmod{5} \implies p \equiv 3 \pmod{5}\)

The answer is D
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6558
Re: If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the  [#permalink]

Show Tags

New post 24 Nov 2016, 20:42
1
2
stonecold wrote:
If \(p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3\),what will be the remainder when p is divided by 5?

A)zero
B)one
C)two
D)three
E)four


Hi
The best way would be UNIT digit..

But another easier way would be to know \(a^3+b^3\) is always div by a+b..
So put the equation in that pair
\(p=1^3+3^3+(5^3) +(9^3 +11^3) +(7^3+13^3)\),
Here only 1^3+3^3 is left..
=1+27=28..
Remainder is 28-25=3
D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Current Student
User avatar
S
Joined: 28 Nov 2014
Posts: 887
Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Reviews Badge
Re: If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the  [#permalink]

Show Tags

New post 25 Nov 2016, 03:47
stonecold wrote:
If \(p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3\), what will be the remainder when p is divided by 5?

A) zero
B) one
C) two
D) three
E) four

When p/5, remainder = 1 + 2 + 0 + 3 + 4 + 1 + 2 = 13
= 13/5

Remainder = 3

Sent from my GT-N7100 using GMAT Club Forum mobile app
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7776
Premium Member
Re: If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the  [#permalink]

Show Tags

New post 16 Dec 2017, 06:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the &nbs [#permalink] 16 Dec 2017, 06:43
Display posts from previous: Sort by

If p=1^3+3^3+5^3 +7^3 +9^3 +11^3 +13^3, what will be the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.