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

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

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10 Apr 2009, 07:31
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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.
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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,
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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
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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.

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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.
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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.
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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
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11 Apr 2009, 14:21
remainder is 2

72/7= 10+ 2/7
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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.
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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.
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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.
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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.
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Please kudos if my post helps.

Re: Remainder - GMATPrep2   [#permalink] 21 Oct 2009, 19:17
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