It is currently 18 Oct 2017, 00:52

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If t is a positive integer and r is the remainder when

Author Message
Director
Joined: 29 Aug 2005
Posts: 855

Kudos [?]: 487 [0], given: 7

If t is a positive integer and r is the remainder when [#permalink]

### Show Tags

10 Apr 2009, 07:31
00:00

Difficulty:

(N/A)

Question Stats:

50% (03:47) correct 50% (02:05) wrong based on 8 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

EDIT: there was a typo - now corrected.

Last edited by seofah on 10 Apr 2009, 23:46, edited 1 time in total.

Kudos [?]: 487 [0], given: 7

Senior Manager
Joined: 08 Jan 2009
Posts: 326

Kudos [?]: 176 [0], given: 5

### Show Tags

10 Apr 2009, 19:13
t>0 and r is rem when t^2+5t+6 is divided by 7

Stmt 1 :
t = 7q + 6
t^2+5t+6 = 49q^2 + 119q + 72
when divided by 7 will leave r = 2. sufficient.

Stmt 2 :

t = 7q + 1
t^2+5t+6 = 49q^2 + 49q + 13
therefore r = 13 . Sufficient

Ans D,

Kudos [?]: 176 [0], given: 5

Current Student
Joined: 13 Jan 2009
Posts: 365

Kudos [?]: 144 [0], given: 1

Location: India

### Show Tags

11 Apr 2009, 03:52
I would go with

1 as tk suggested
while for option 2 we have various choices

Lets says t^2=36 and 64
per statement 2 rem(t^2/7)=1

5*6+6; 5*8+6
rem(6)=1; rem(4) inconsistent.

Ans A

Kudos [?]: 144 [0], given: 1

Manager
Joined: 19 Aug 2006
Posts: 239

Kudos [?]: 13 [0], given: 0

### Show Tags

11 Apr 2009, 10:25
I would go with C.

I think neither of the statements alone is sufficient, because you cannot say e.g. in stmnt1 that t=7q+6 for sure. The quotient here does not have to equal the quotient from the question stem.

Kudos [?]: 13 [0], given: 0

Manager
Joined: 14 Nov 2008
Posts: 195

Kudos [?]: 129 [0], given: 3

Schools: Stanford...Wait, I will come!!!

### Show Tags

11 Apr 2009, 10:47
I hope that some one wil give some short answer.
But as far as solution is concerned, here it is..
But it took me almost 5 minutes.. so .. of course.. i know.. my solution is not advisable.

From one,
t-6 is divisible by 7, implies that t>= 6, but it can have values..6,13,20,27,34 etc..so 1 is not enough
From 2)
t^2 -1 is divisible by 7, implies that t >=6, but this equation is also satisfied by,6,8,13,27,....
So, 2 is also not enough alone.

combining 1 and 2, we have
that t can have value 13,27,...
in both the case, the remainder is 2, hence combing 1 and 2 we cn answer.

botirvoy 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

EDIT: there was a typo - now corrected.

Kudos [?]: 129 [0], given: 3

Current Student
Joined: 13 Jan 2009
Posts: 365

Kudos [?]: 144 [0], given: 1

Location: India

### Show Tags

11 Apr 2009, 13:35
peraspera wrote:
I would go with C.

I think neither of the statements alone is sufficient, because you cannot say e.g. in stmnt1 that t=7q+6 for sure. The quotient here does not have to equal the quotient from the question stem.

t=7k+6
t^2=49k^2+84k+36

t^2+5t+6
49k^2+84k+36+5(7k+6)+6
49k^2+199k+72
rem[72/7]=2
r=2

I dont see any problem with A. If you see some prob let me know I will also correct fundamentals.

Kudos [?]: 144 [0], given: 1

Manager
Joined: 19 Aug 2006
Posts: 239

Kudos [?]: 13 [0], given: 0

### Show Tags

11 Apr 2009, 14:15
hemantsood wrote:
peraspera wrote:
I would go with C.

I think neither of the statements alone is sufficient, because you cannot say e.g. in stmnt1 that t=7q+6 for sure. The quotient here does not have to equal the quotient from the question stem.

t=7k+6
t^2=49k^2+84k+36

t^2+5t+6
49k^2+84k+36+5(7k+6)+6
49k^2+199k+72
rem[72/7]=2
r=2

I dont see any problem with A. If you see some prob let me know I will also correct fundamentals.

Let's see, maybe it's me who needs to correct the fundamentals.
Could you please explain this line: rem[72/7]=2

Kudos [?]: 13 [0], given: 0

Current Student
Joined: 13 Jan 2009
Posts: 365

Kudos [?]: 144 [0], given: 1

Location: India

### Show Tags

11 Apr 2009, 14:21
remainder is 2

72/7= 10+ 2/7

Kudos [?]: 144 [0], given: 1

Manager
Joined: 19 Aug 2006
Posts: 239

Kudos [?]: 13 [0], given: 0

### Show Tags

11 Apr 2009, 15:44
hemantsood wrote:
remainder is 2

72/7= 10+ 2/7

I think you are correct, stmnt 1 is sufficient. I got confused while picking numbers.
I got that stmnt 2 is sufficient as well, though. Could you explain a deficiency:

t^2=7k+1
t=sqrt(7k+1)
t^2+5t+6=7k^2+7K+38
38/7=5*7+3
r=3

Last edited by peraspera on 11 Apr 2009, 17:36, edited 1 time in total.

Kudos [?]: 13 [0], given: 0

Current Student
Joined: 13 Jan 2009
Posts: 365

Kudos [?]: 144 [0], given: 1

Location: India

### Show Tags

11 Apr 2009, 16:10
peraspera wrote:
hemantsood wrote:
remainder is 2

72/7= 10+ 2/7

I think you are correct, stmnt 1 is sufficient. I got confused while picking numbers.
I got that stmnt 2 is sufficient as well, though. Could you explain a deficiency:

t^2=7k+1
t=sqrt(7k+1)
t^2+5t+6=7k^2+7K+36
38/7=5*7+3
r=3

Thats not neat

t^2+5t+6=7k+1+5sqrt(7k+1)+6
=7k+7+5sqrt(7k+1)

now result will vary with k as this is only factor that would be driving remainder everything else in mutlitple of 7.

Here different values of k will result in different value of r, there fore, this is not suff.

Kudos [?]: 144 [0], given: 1

Manager
Joined: 14 Nov 2008
Posts: 195

Kudos [?]: 129 [0], given: 3

Schools: Stanford...Wait, I will come!!!

### Show Tags

12 Apr 2009, 04:12
hemantsood wrote:
peraspera wrote:
hemantsood wrote:
remainder is 2

72/7= 10+ 2/7

I think you are correct, stmnt 1 is sufficient. I got confused while picking numbers.
I got that stmnt 2 is sufficient as well, though. Could you explain a deficiency:

t^2=7k+1
t=sqrt(7k+1)
t^2+5t+6=7k^2+7K+36
38/7=5*7+3
r=3

Thats not neat

t^2+5t+6=7k+1+5sqrt(7k+1)+6
=7k+7+5sqrt(7k+1)

now result will vary with k as this is only factor that would be driving remainder everything else in mutlitple of 7.

Here different values of k will result in different value of r, there fore, this is not suff.

Thanks.. that was good..
Although, we can .. take your last expression..
7k +7+ 5 sqrt(7k+1)
Now, the only thing that contribute the remainder is 5 sqrt(7k+1)
but sqrt(7k+1 ) = t
so.. it is 5t/7... and t > 0.. so it can have multiple values...
It was just a perspective....Not done anything from my side.

Kudos [?]: 129 [0], given: 3

Manager
Joined: 22 Jul 2009
Posts: 191

Kudos [?]: 281 [2], given: 18

### Show Tags

21 Oct 2009, 19:17
2
KUDOS
Here's a different approach, which took me 30 seconds:

1st. t^2+5t+6 = (t+2)(t+3) (easy to spot this one)

2nd. Work the other way around: stat1 says t=7k+6
=> t+2=7k+8 =8k+1, and t+3=7k+9 =8k+2
=>(8k+1)(8k+2) => r=1*2 => remainder is always 2

For statement 2, it was obvious to me that it was not sufficient, so quickly tried so numbers and got that the condition was valid for both 6^2 and 8^2. I like hemantsood's algebraic approach.

btw, this is a gprep problem.
_________________

Please kudos if my post helps.

Kudos [?]: 281 [2], given: 18

Re: Remainder - GMATPrep2   [#permalink] 21 Oct 2009, 19:17
Display posts from previous: Sort by