Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 26 May 2017, 08:18

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If t is a positive integer and r is the remainder when t^2+5

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

Hide Tags

3 KUDOS received
Intern
Intern
avatar
Joined: 20 Feb 2012
Posts: 13
Followers: 0

Kudos [?]: 26 [3] , given: 2

If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 23 Feb 2012, 15:21
3
This post received
KUDOS
25
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

52% (02:47) correct 48% (01:56) wrong based on 947 sessions

HideShow timer Statistics

If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

(1) When t is divided by 7, the remainder is 6.
(2) When t^2 is divided by 7, the remainder is 1.

[Reveal] Spoiler:
...
(1) means t=7n+6.
=> t²=(7n+6)²)=49n²+84n+36=49n²+84n+35+1
=> 5t=35n+30=35n+28+2

remainders 1+2+6=9=7+2

Remainder of t²+5t+6 is 2????

I dont really get this -.-
[Reveal] Spoiler: OA
Expert Post
8 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38898
Followers: 7739

Kudos [?]: 106205 [8] , given: 11610

If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 23 Feb 2012, 15:50
8
This post received
KUDOS
Expert's post
16
This post was
BOOKMARKED
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

First of all factor \(t^2+5t+6\) --> \(t^2+5t+6=(t+2)(t+3)\).

(1) When t is divided by 7, the remainder is 6 --> \(t=7q+6\) --> \((t+2)(t+3)=(7q+8)(7q+9)\). Now, no need to expand and multiply all the terms, just notice that when we expand all terms but the last one, which will be 8*9=72, will have 7 as a factor and 72 yields the remainder of 2 upon division by 7. Sufficient.

(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in \((t+2)(t+3)\) will give different remainder upon division by 7. Not sufficient.

Answer: A.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Intern
Intern
User avatar
Joined: 23 Dec 2012
Posts: 7
Concentration: General Management, Entrepreneurship
GPA: 3.5
WE: Consulting (Non-Profit and Government)
Followers: 0

Kudos [?]: 8 [2] , given: 12

Reviews Badge
Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 08 Feb 2013, 10:37
2
This post received
KUDOS
My approach:

From (1) - t/7 gives remainder = 6. So we can easily find remainder for t^2 and 5*t in the algebraic exp. t^2 + 5t + 6 using properties of remainder.

Therefore the remainder of algebraic exp. = 1 + 2 + 6 = 9 (7 + 2) = 2 ................. [A]


Properties of remainder:

[1] If a quotient is squared, the remainder also gets squared and we need to adjust the new remainder based on no. we get on squaring.

Here quotient = t, r = 6. So, t^2 will have r' = 36 (7*5 + 1). Therefore r' =1

[2] If a quotient is multiplied by an integer k , the remainder also gets multiplied and we need to adjust the new remainder based on no. we get on multiplication.

Here quotient = t, r = 6. So, 5t will have r'' = 30 (7*4 + 2). Therefore r'' = 2

We get [A] using [1] and [2].

Clearly Stmt (2) can have multiple possibilities i.e. if t= 1 (t^2 =1) and t =6 (t^2 = 36) both give remainder 1, so no unique answer and hence rejected.

Thus A is the answer.
Expert Post
1 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38898
Followers: 7739

Kudos [?]: 106205 [1] , given: 11610

Re: Tricky? remainder question (gmatprep) [#permalink]

Show Tags

New post 05 Jul 2012, 11:28
1
This post received
KUDOS
Expert's post
carcass wrote:
Bunuel wrote:
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

First of all factor t^2+5t+6 --> t^2+5t+6=(t+2)(t+3)

(1) When t is divided by 7, the remainder is 6 --> t=7q+6 --> (t+2)(t+3)=(7q+8)(7q+9). Now, no need to expand and multiply all the terms, just notice that when we expand all terms but the last one, which will be 8*9=72, will have 7 as a factor and 72 yields the remainder of 2 upon division by 7. Sufficient.

(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in (t+2)(t+3) will yield different remainder upon division by 7. Not sufficient.

Answer: A.

Hope it's clear.



Sorry Bunuel but this part highlighted is not completely clear: on the left side of = we have the two roots of our equation; on the right (t+2) ----> is 7q+6+2 ---> 7q+8 (same reasoning for 7q+9) BUT why we equal this two part ?? Can you explain me please ??

Thank you


We are asked to find the remainder when \(t^2+5t+6\) is divided by 7 or as \(t^2+5t+6=(t+2)(t+3)\), the remainder when \((t+2)(t+3)\) is divided by 7.

Now, from (1) we have that \(t=7q+6\). Substitute \(t\) with \(7q+6\) in \((t+2)(t+3)\) to get \((7q+8)(7q+9)\). So, finally we have that we need to find the remainder when \((7q+8)(7q+9)\) is divided by 7 (\(t^2+5t+6=(t+2)(t+3)=(7q+8)(7q+9)\)).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Manager
Manager
User avatar
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 179
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22
GPA: 3.1
Followers: 3

Kudos [?]: 146 [1] , given: 623

GMAT ToolKit User
Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 06 Sep 2014, 05:17
1
This post received
KUDOS
Shehryar Khan wrote:
(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in (t+2)(t+3) will give different remainder upon division by 7. Not sufficient.

Bunuel could you please explain why statement 2 is not sufficient and how the values for 't' could be either 1 or 6?


Hii Shehryar khan,
let me try to explain..

t^2/7=1----------given

as u can see,we have 2 values of 2..1^2/7=remainder 1 and 6^2/7=36/7=remainder 1..
when we substitute 1 in (t+2)(t+3)/7 ,we get remainder as 5..
when we substitute 6 in (t+2)(t+3)/7, we get remainder as 2..

So,since the results are inconsistent,we cant have one definite remainder,which we are required to find,as per the stem..so,not sufficient..

Please consider KUDOS if my post helped :)
_________________

ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.

Moderator
Moderator
User avatar
S
Joined: 01 Sep 2010
Posts: 3174
Followers: 858

Kudos [?]: 7310 [0], given: 1065

Re: Tricky? remainder question (gmatprep) [#permalink]

Show Tags

New post 05 Jul 2012, 11:18
Bunuel wrote:
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

First of all factor t^2+5t+6 --> t^2+5t+6=(t+2)(t+3)

(1) When t is divided by 7, the remainder is 6 --> t=7q+6 --> (t+2)(t+3)=(7q+8)(7q+9). Now, no need to expand and multiply all the terms, just notice that when we expand all terms but the last one, which will be 8*9=72, will have 7 as a factor and 72 yields the remainder of 2 upon division by 7. Sufficient.

(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in (t+2)(t+3) will yield different remainder upon division by 7. Not sufficient.

Answer: A.

Hope it's clear.



Sorry Bunuel but this part highlighted is not completely clear: on the left side of = we have the two roots of our equation; on the right (t+2) ----> is 7q+6+2 ---> 7q+8 (same reasoning for 7q+9) BUT why we equal this two part ?? Can you explain me please ??

Thank you
_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks

Moderator
Moderator
User avatar
S
Joined: 01 Sep 2010
Posts: 3174
Followers: 858

Kudos [?]: 7310 [0], given: 1065

Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 05 Jul 2012, 15:58
Senior Manager
Senior Manager
User avatar
Joined: 13 Jan 2012
Posts: 307
Weight: 170lbs
GMAT 1: 740 Q48 V42
GMAT 2: 760 Q50 V42
WE: Analyst (Other)
Followers: 17

Kudos [?]: 167 [0], given: 38

Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 06 Nov 2013, 09:34
Wow. This is a tough problem. A is straightforward once you see it. B is time consuming if you take it all the way.
Intern
Intern
avatar
Joined: 15 Aug 2014
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 6

If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 25 Aug 2014, 12:51
1
This post was
BOOKMARKED
(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in (t+2)(t+3) will give different remainder upon division by 7. Not sufficient.

Bunuel could you please explain why statement 2 is not sufficient and how the values for 't' could be either 1 or 6?
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15462
Followers: 649

Kudos [?]: 209 [0], given: 0

Premium Member
Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 03 Oct 2015, 17:15
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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15462
Followers: 649

Kudos [?]: 209 [0], given: 0

Premium Member
Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 14 Oct 2016, 15:13
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

Math Forum Moderator
User avatar
S
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2678
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Followers: 111

Kudos [?]: 860 [0], given: 324

GMAT ToolKit User Premium Member
If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 15 Oct 2016, 07:31
dpark wrote:
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

(1) When t is divided by 7, the remainder is 6.
(2) When t^2 is divided by 7, the remainder is 1.


FROM STATEMENT - I INSUFFICIENT

The minimum value of t = 13

So, \(t^2+5t+6 = 13^2+5*13+6\) = \(240\)

Now, \(\frac{240}{7}\) = Remainder 2

FROM STATEMENT - II INSUFFICIENT

The minimum value of t = +1 and -1

So, \(t^2+5t+6 = 1^2+5*1+6\) = \(12\) Remainder 5

And \(t^2+5t+6 = -1^2+5*-1+6\) = \(2\) Remainder 2

Thus, Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked, hence correct answer will be (A)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Intern
User avatar
B
Joined: 19 Sep 2012
Posts: 13
Followers: 0

Kudos [?]: 1 [0], given: 5

CAT Tests
If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 04 Jan 2017, 04:14
I am sure that I am missing something because stem (1) tells that t=7q+6 so t=6,13,20,...
then we can try different values of t so that we can find out the reminder,
so it follows that (t+2)(t+3)=5p+r
for t=13 (13+2)(13+3)=240, 240/5 gives a reminder of 0
for t=20 (20+2)(20+3)=506, 506/5 gives a reminder of 1.
So stem (1) Not sufficient...
Please, can someone explain to me what I am missing? Thanks
Senior Manager
Senior Manager
User avatar
S
Joined: 26 Oct 2016
Posts: 460
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Followers: 25

Kudos [?]: 63 [0], given: 823

Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]

Show Tags

New post 11 Feb 2017, 23:58
First, solve the equation

t^2 + 5t + 6 = (t+2)(t+3)

statement (1)

t = 7q + 6
t can also be written as 7k-1, this means any multiple of 7 and then subtract 1 to the same when divided by 7 will always give a remainder 6

therefore,

(t+2)(t+3) = (7k-1+2)(7k-1+3) = (7k+1)(7k+2)

when (7k+1) will be divided by 7 the remainder will be 1
when (7k+2) will be divided by 7 the remainder will be 2

when the product of both is divided by 7 the remainder will be 2 for any value of k.
Sufficient.

Statement (2)
t^2 when divided by 7 the remainder is 1
We cannot follow the same strategy as above in this statement because here we are dealing with addition as compared to multiplication as statement (1)

this statement is even more simpler than the first one

t^2 + 5t + 6
t^2 = multiple of 7 + 1

t^2 + 6 = multiple of 7.

Therefore, we only have to find out if 5t/7 gives standard remainder across all cases.

5*5/7 = 35/7 = remainder 0
5*4/7 = 20/7 = remainder 6
5*6/7 = 30/7 = remainder 2.

Insufficient.
_________________

Thanks & Regards,
Anaira Mitch

Re: If t is a positive integer and r is the remainder when t^2+5   [#permalink] 11 Feb 2017, 23:58
    Similar topics Author Replies Last post
Similar
Topics:
10 Experts publish their posts in the topic If r is the remainder when the positive integer n is divided vigneshpandi 8 03 Apr 2016, 21:23
46 Experts publish their posts in the topic If n is a positive integer, and r is the remainder when LM 29 30 Jan 2017, 22:58
7 Experts publish their posts in the topic If n is a positive integer and r is the remainder when (n - ksharma12 7 22 Apr 2017, 01:22
19 Experts publish their posts in the topic If n is a positive integer and r is remainder, when kyatin 15 18 May 2015, 04:58
5 Experts publish their posts in the topic If t is a positive integer and r is the remainder when t^2 + marcodonzelli 7 16 Aug 2013, 01:36
Display posts from previous: Sort by

If t is a positive integer and r is the remainder when t^2+5

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


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.