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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.

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.

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. C is the 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

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.

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.

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:

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:

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:

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.

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.