patio-d wrote:If t is a postive integer and r is the remainder when t-squared+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-squared is divided by 7, the remainder is 1.
How to solve this without taking heaps of time?
Thank you!
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well if I understand you correctly, you already know how to solve this problem but you are looking for a faster approach.
Question wants you to find R:
t-squared+5t+6 = 7(integer) + R
so in other words, if you can change the left side of the question into 7A+R format, R is your answer!
and you need to see that t-squared+5t+6 = (t+3)(t+2) in case!
1) t = 7a+ 6
(7a+9)(7a+8)divided by 7
(7a+7+
2)(7a+7+
1) ; so the remainder will always be 2.
SUFF
2) t-squared = 7b+1
t-squared - 1 = 7b
(t-1)(t+1) = 7b
t will have two values, and for each T value the Remainder will change
Insuf
IMO, hence A
It might be D , if I missed something in statement 2
