December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 13

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
23 Feb 2012, 14:21
Question Stats:
53% (01:53) correct 47% (01:54) wrong based on 1406 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. ... (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 .
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51121

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
23 Feb 2012, 14:50
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: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics




Board of Directors
Joined: 01 Sep 2010
Posts: 3292

Re: Tricky? remainder question (gmatprep)
[#permalink]
Show Tags
05 Jul 2012, 10:18
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 ALLINONE 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. Readingcomprehension_Oldy but goldy question banks



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: Tricky? remainder question (gmatprep)
[#permalink]
Show Tags
05 Jul 2012, 10:28
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: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 23 Dec 2012
Posts: 6
Concentration: General Management, Entrepreneurship
GPA: 3.5
WE: Consulting (NonProfit and Government)

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
08 Feb 2013, 09:37
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.



Intern
Joined: 15 Aug 2014
Posts: 1

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
25 Aug 2014, 11:51
(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?



Manager
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 148
Location: India
Concentration: General Management, Finance
GPA: 3.1

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
06 Sep 2014, 04:17
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=1given 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.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4274
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
15 Oct 2016, 06:31
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 INSUFFICIENTThe 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 INSUFFICIENTThe 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
Joined: 19 Sep 2012
Posts: 12

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
04 Jan 2017, 03:14
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



Director
Joined: 26 Oct 2016
Posts: 640
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
11 Feb 2017, 22:58
First, solve the equation t^2 + 5t + 6 = (t+2)(t+3) statement (1) t = 7q + 6 t can also be written as 7k1, 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) = (7k1+2)(7k1+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



Manager
Joined: 21 Mar 2017
Posts: 141
Location: India
WE: Other (Computer Software)

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
22 Aug 2017, 05:04
Hi Bunuel , As t^2 = 7m+1 so t^2 could be 1,8,15,22. Which gives the remainder as 5. But you have taken the value as 1 and 6. Could you please explain why you have taken 6 instead of 8 in case 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)(t+2)(t+3) will give different remainder upon division by 7.
_________________
 When nothing seem to help, I would go and look at a Stonecutter hammering away at his rock perhaps a hundred time without as much as a crack showing in it. Yet at the hundred and first blow it would split in two. And I knew it was not that blow that did it, But all that had gone Before.



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
22 Aug 2017, 06:01
Prashant10692 wrote: Hi Bunuel , As t^2 = 7m+1 so t^2 could be 1,8,15,22. Which gives the remainder as 5. But you have taken the value as 1 and 6. Could you please explain why you have taken 6 instead of 8 in case 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)(t+2)(t+3) will give different remainder upon division by 7. (2) reads: t^2 is divided by 7, the remainder is 1, not t. t = 1 > t^2 = 1 > 1 divided by 7 gives the remainder of 1. t = 6 > t^2 = 36 > 36 divided by 7 gives the remainder of 1.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 04 Feb 2017
Posts: 13

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
19 Apr 2018, 12:23
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 give different remainder upon division by 7. Not sufficient.
Answer: A.
Hope it's clear. Hi BunuelIn terms of approach, can you clarify how one should look at the two statements? That is, your approach with st 1 is kind of algebraic and the latter was number plugging in. The former is a bit intuitive in this case (for me at least) but then how do you decide which approach befits statement 2 for instance?



Manager
Joined: 10 Apr 2018
Posts: 180

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
06 Sep 2018, 12:24
Abhishek009 wrote: 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 INSUFFICIENTThe 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 INSUFFICIENTThe 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)
Hi Abhishek009Well why can't the min value of t=6 Probus



Manager
Joined: 10 Apr 2018
Posts: 180

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
06 Sep 2018, 12:44
VikramJS wrote: 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. Hi Bunuel, Can you explain how above has been used to arrive at answer. I think the user wanted to convey dividend in place of quotient Thnaks Probus



Manager
Joined: 10 Apr 2018
Posts: 180

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
06 Sep 2018, 13:56
Hi chetan2u, For this question is this approach correct we can write the exp as (t+2)(t+3) Stm1:\(\frac{t}{7}\) gives reminder 6, then it must be that (t+1) will give reminder 0, and (t+2) &(t+3) will give reminder 1,2 respectively then reminder is equal to 2 Sufficient Stmt 2: \(t^2\) divided by 7 gives reminder 1 , t could take value of 1 or 6 then exp gives different reminders. Not Suff My concern is regarding the approach used for Stmt 1. Is it correct Probus



Intern
Joined: 03 Apr 2017
Posts: 45

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
08 Sep 2018, 00:35
Please help me out in this one as I have a lapse in my understanding.
I always thought the following to be true:
Here simplifying k^2 where k leaves a remainder of 1 with 7, the values of k can be 1 or 6; I thought we could apply the general rule that if 2 elements are multiplied, the remainder of the expression would be the remainder of the product of the individual remainders of each term of the expression.
For example, if we have an expression say 9k, and we know that k when divided by 7 is 1, then the following would be the remainder when 9k is divided by 7.
Remainder of 9 with 7 will be 2 Remainder of k with 7 will be 1
Multiplying remainders is 9k = 2 * 1 = 2 Thus the remainder of the expression 9k would be 2 when divided by 7
So extending that logic, if the expression is k^2, the remainder should be
1 * 1 = 1, thus the remainder would be 1. But clearly this is not the case as seen here, as 6 is also a valid answer.
I guess the core of my question is the above method that I used, is it outright wrong? Or is it applicable only in cases where expressions are of the form constant * variable like 9k and not when it is of the form variable * variable like k^2.



Intern
Joined: 26 Dec 2016
Posts: 11

If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
30 Sep 2018, 21:19
BunuelCan you please help in clearing my confusion statement2: t^2=7q+1 substituting in the given equation t^2+5t+6 (7q+1+5t+6)/7 (7q+5t+7)/7 (7(q+1)+5t)/7 5t+0 so remainder 0.... why don't we use this method?



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
30 Sep 2018, 22:01



Intern
Joined: 21 Nov 2016
Posts: 36

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
Show Tags
30 Sep 2018, 22:15
From statement 1 we have t/7 the remainder is 6 t = 7k + 6 Going by the equation in question t^2 = (7k+6)^2 = 49k^2+36+84k Next, t^2+5t = 49k^2+36+84k+5(7k+6) = 49k^2+36+84k+35k+30 Next, t^2+5t+6= 49k^2+36+84k+35k+30+6 = 49k^2+36+84k+35k+36 Implies, t^2+5t+6 = 7(7k^2+12k+5k)+72 = 7(7k^2+17k)+7(10)+2 Implies, t^2+5t+6= 7(7k^2+17k+10)+2 This implies that the remainder r = 2. So, Statement 1 is sufficient. From statement 2 we have t^2 =7x+1 Implies , t = (7x+1)^1/2 If the above result is substituted in the equation in the question stem then we get t^2+5t+6 = 7x+1+5((7x+1)^1/2)+6 which cannot be simplified further elegantly. So the answer is A.




Re: If t is a positive integer and r is the remainder when t^2+5 &nbs
[#permalink]
30 Sep 2018, 22:15



Go to page
1 2
Next
[ 22 posts ]



