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If t is a positive integer and r is the remainder when [#permalink]
10 Apr 2009, 06:31
50% (04:47) correct
50% (02:05) wrong based on 8 sessions
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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, 22:46, edited 1 time in total.
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.
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
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.