Fistail wrote:
fresinha12 wrote:
I dont think this is that hard...
asks what is r if (t+3)(t+2) is divided by 7!
1) says t=7N+6
so (t+3)=7N+9 => 7(N+1)+2
(t+2) => 7N+8 => 7(N+1)+1
so you will notice that r will always be 2... for any value of N...
sufficient
2) t^2=7N+1
t=6 then in that case (9)(8)/7 gives remainder 2...
t can also be 8... in that case (10)(11)/7 gives remainder 5..insuff
A it is..
excellent approach..
agree with A.
can be done this way as well:
1: since t has 6 reminder if t is divided by 7, t = 7k +6.
= t^2 + 5t + 6
= (7k+6)(7k+6) + 5 (7k+6) + 6
= 49k^2 + 42k + 42k + 36 + 35k + 30 + 6
= 49k^2 + 119k + 72
in the above expression, 49k^2 and 119k are evenly divided by 7. so remains 72 which as 2 as reminder when it is divided by 7.
so suff...
2: t^2 has 1 reminder if t^2 is divided by 7.
t could be 6 or 8 or 15 each has 1 as reminder so the reminder of the expression t^2 + 5t + 6 is different with t values. nsf.
A.
I think these approaches are too time consuming. I just finished my GMAT today and I saw a problem VERY VERY similar to this question. The general idea/concept was the same, but the quadratic and divisor was different. Here's my take on how to approach (1):
The quadratic factors to: (t + 2)(t +3)
hmm...what pattern have we consistently seen involving divisors and quadratics? I'm thinking consecutive integers.
(1) Provides info on t so add to this consecutive integer string: t, t + 1, t + 2, t + 3
we know t has a remainder 6 when divided by 7 so t + 1 MUST be divisible by 7 which means t + 2 will have a remainder of 1 when divided by 7 and t + 3 will have a remainder of 2 when divided by 7. How do I know this? Simple: remainders increase from 0 to x - 1 as you iterate over consecutive integers and reset back to 0 once you reach a number that divides evenly. 7%7 = 0, 8%7 = 1, 9%7 = 2 etc etc where % is the modulus function (gives the remainder).
So now pick two values for t + 2 and t + 3 which have remainders 1 and 2, respectively.
8 and 9: 8*9 = 72; 72%7 = 2
15 and 16: 15*16 = 240%7 = 2
etc etc
SUFF. This method is simple, easy to understand and just involves picking numbers - no long winded quadratic calculations necessary.
(2) I'm not going to discuss because I just wanted to mention how I solved for (1)